(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 284954, 8254]*) (*NotebookOutlinePosition[ 285615, 8277]*) (* CellTagsIndexPosition[ 285571, 8273]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Calcolo di sollecitazioni e spostamenti in un sistema di travi rettilinee\ \>", "Title"], Cell["\<\ Anche se non sembra semplice assegnare i dati conviene leggere le istruzioni \ ed evitare adattamenti con conseguenze imprevedibili\ \>", "Subtitle", CellFrame->True, Evaluatable->False, CellHorizontalScrolling->False, TextAlignment->Left, FontSize->12, Background->GrayLevel[0.849989]], Cell[TextData[StyleBox["v. 2.02 (10/4/2003) \n\[Copyright] Amabile Tatone, \ Universit\[AGrave] dell'Aquila, L'Aquila, IT \ntatone@ing.univaq.it", FontSize->14, FontWeight->"Bold"]], "Subtitle", CellFrame->True, Evaluatable->False, CellHorizontalScrolling->False, TextAlignment->Left, FontSize->12, Background->GrayLevel[0.849989]], Cell[CellGroupData[{ Cell["Istruzioni", "Section", Evaluatable->False], Cell[TextData[{ "Sono da assegnare:\n- i vettori a1 e a2 della base adattata alla sezione \ [", StyleBox["D1", FontColor->RGBColor[0, 0, 1]], "]\n- la distribuzione di forza [", StyleBox["D2", FontColor->RGBColor[0, 0, 1]], "]\n- i vincoli e le basi adattate al bordo [", StyleBox["D3", FontColor->RGBColor[0, 0, 1]], "]\n- le forze e i momenti alle estremit\[AGrave] [", StyleBox["D4", FontColor->RGBColor[0, 0, 1]], "]\n- costanti (lunghezze, moduli, intensit\[AGrave] delle forze) [", StyleBox["D5", FontColor->RGBColor[0, 0, 1]], "]\n\nSono da adattare:\n- la funzione di semplificazione extraSimplify [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]\n- la cornice per la visualizzazione della deformazione [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]\n- i fattori di scala per i diagrammi tecnici N, Q, M [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]\n\nSono da controllare:\n- alcune definizioni riguardanti \ semplificazioni" }], "SmallText", CellFrame->True, Background->GrayLevel[0.849989]], Cell["\<\ Viene prima calcolata la soluzione bulk delle equazioni di bilancio in \ corrispondenza di una qualsiasi distribuzione di forze (integrabile). Vengono assegnati i vincoli. Esiste il problema di compatibilita' dei vincoli \ solo in forma banale. Non esiste certamente per gli atti di moto, essendo per \ questi i vincoli delle condizioni omogenee. Vengono poi costruite le equazioni di bilancio al bordo corrispondenti agli \ atti di moto vincolati, fornendo l'elenco delle forze attive da assegnare. Sostituendo in queste equazioni la soluzione bulk si generano delle equazioni \ algebriche nelle costanti di integrazione. Viene calcolata la soluzione che, nel caso di \"vincoli eccedenti\", lascia \ indeterminate alcune delle costanti. Si puo' dire che si determina lo spazio delle soluzioni in termini di \ tensione bilanciata al bordo. In caso di \"vincoli in difetto\" occorre verificare la compatibilit\[AGrave] \ dei dati al bordo sulle forze. Si prosegue calcolando, attraverso la funzione di risposta, lo spazio degli \ spostamenti corrispondente alla tensione, introducendo altre costanti di \ integrazione. Dalle equazioni di vincolo si generano le equazioni algebriche da cui si \ calcolano infine tutte le costanti. Vincoli \"eccedenti\" => equazioni di bilancio al bordo \"in difetto\" Vincoli \"in difetto\" => equazioni di bilancio al bordo \"eccedenti\" \ (occorre verificare la compatibilita' delle forze al bordo)\ \>", "SmallText", CellFrame->True, Background->GrayLevel[0.849989]], Cell[TextData[{ "Le lunghezze dei vari tratti possono essere assegnate utilizzando una \ lunghezza base (ad esempio ", StyleBox["\[ScriptCapitalL]", FontFamily->"Courier"], " ), in modo che non compaiano in tutte le espressioni ", StyleBox["L[1], L[2]", FontFamily->"Courier"], " ecc.; cos\[IGrave] pure gli angoli. Occorre poi assegnare i valori di \ tali parametri in datiO per poter realizzare le figure." }], "SmallText", CellFrame->True, Background->GrayLevel[0.849989]] }, Closed]], Cell[CellGroupData[{ Cell["Inizializzazione", "Section", Evaluatable->False], Cell[BoxData[ \(\(outputDir = \ "\";\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(SetDirectory[outputDir]\)], "Input"], Cell[BoxData[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-11a\\outmath"\)], "Output"] }, Open ]], Cell["\<\ In fase di modifica del notebook riattivare gli \"spelling warning\"\ \>", "SmallText"], Cell[BoxData[{ \(\(Off[General::"\"];\)\), "\[IndentingNewLine]", \(\(Off[General::"\"];\)\)}], "Input"], Cell[BoxData[{ \(\(Off[Solve::"\"];\)\), "\n", \(\(<< \ LinearAlgebra`MatrixManipulation`;\)\), "\[IndentingNewLine]", \(\(<< Graphics`Colors`;\)\), "\n", \(\(SetOptions[Plot, ImageSize \[Rule] 228];\)\), "\n", \(\(SetOptions[ParametricPlot, ImageSize \[Rule] {200, 200}];\)\), "\[IndentingNewLine]", \(\(SetOptions[Plot, PlotRange \[Rule] All];\)\), "\[IndentingNewLine]", \(\(SetOptions[ParametricPlot, PlotRange \[Rule] All];\)\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Descrizione della configurazione originaria [", StyleBox["D1", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Definizione delle basi", "Subsection", CellFrame->False, Background->None], Cell["Base del sistema di coordinate (non modificare)", "SmallText", CellFrame->False, Background->None], Cell[BoxData[{ \(\(e\_1 = {1, 0};\)\), "\n", \(\(e\_2 = {0, 1};\)\)}], "Input", CellFrame->False, Background->None], Cell["\<\ Basi adattate alla sezione di ciascun tratto (non modificare)\ \>", "SmallText", CellFrame->False, Background->None], Cell[BoxData[{ \(\(a\_1[i_] := Cos[\[Alpha][i]]\ e\_1 + Sin[\[Alpha][i]]\ e\_2;\)\), "\n", \(\(a\_2[i_] := \(-Sin[\[Alpha][i]]\)\ e\_1 + Cos[\[Alpha][i]]\ e\_2;\)\)}], "Input", CellFrame->False, Background->None] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Dati [", StyleBox["D1", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell["Numero di tratti di trave", "SmallText"], Cell[BoxData[ \(\(travi = 1;\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[TextData[{ "Angoli che definiscono le basi adattate (possono anche non essere \ assegnati; in tal caso se ne assegni il valore nella lista ", StyleBox["datiO", FontFamily->"Courier New", FontWeight->"Bold"], ")\n", "[ l'uso di caratteri script per i parametri rende tutto molto pi\[UGrave] \ leggibile]" }], "SmallText", FontFamily->"Arial"], Cell[BoxData[ \(\(\[Alpha][1] = \(-3\) \[Pi]\/4;\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[TextData[{ "Lunghezze (possono anche non essere assegnate; in tal caso se ne assegni \ il valore nella lista successiva ", StyleBox["datiO", FontFamily->"Courier New", FontWeight->"Bold"], ")\n", "[ l'uso caratteri script per i parametri rende tutto molto pi\[UGrave] \ leggibile]" }], "SmallText"], Cell[BoxData[ \(\(L[1] = \[ScriptCapitalL];\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[{ \(YA[1] := \[ScriptCapitalY]\[ScriptCapitalA]\ \ \), \ "\[IndentingNewLine]", \(YJ[1] := \[ScriptCapitalY]\[ScriptCapitalJ]\)}], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell["\<\ Valori numerici (di angoli e lunghezze) necessari alla visualizzazione e \ utilizzati solo per questo\ \>", "SmallText"], Cell[BoxData[ \(\(datiO = {\[ScriptCapitalL] \[Rule] 1};\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell["\<\ Altri dati EVENTUALMENTE assegnati (anche per ottenere espressioni \ pi\[UGrave] semplici). \ \>", "SmallText"], Cell[BoxData[ \(\[ScriptCapitalY]\[ScriptCapitalA] := \ \[ScriptCapitalY]\[ScriptCapitalJ]\/\(\[Kappa]\ \[ScriptCapitalL]\^2\)\)], \ "Input", CellFrame->True, Background->GrayLevel[0.849989]] }, Closed]], Cell[CellGroupData[{ Cell["Definizioni per la visualizzazione", "Subsection"], Cell["lunghezza caratteristica", "SmallText"], Cell[BoxData[ \(\(maxL = Max[Table[ L[i] /. \[InvisibleSpace]datiO, {i, 1, travi}]];\)\)], "Input"], Cell["definizione dell'asse", "SmallText"], Cell[BoxData[ \(\(\(\(asseO[i_]\)[\[Zeta]_] := org[i] + a\_1[i]\ \[Zeta] /. datiO;\)\(\ \)\)\)], "Input"], Cell[BoxData[ \(Clear[org]\)], "Input"], Cell["\<\ Coordinate dell'estremit\[AGrave] sinistra di ciascun tratto (utilizzate solo \ per la visualizzazione dei tratti separati). Quelle deivanti dai vincoli sono \ descritte a parte, pi\[UGrave] avanti.\ \>", "SmallText"], Cell[BoxData[ \(\(org[1] = {0, 0};\)\)], "Input"], Cell[BoxData[ \(org[i_] := org[i - 1] + {Max[\(\(asseO[i - \ 1]\)[0]\)\_\(\(\[LeftDoubleBracket]\)\(1\)\(\[RightDoubleBracket]\)\), \ \(\(asseO[i - 1]\)[L[i - 1]]\)\_\(\(\[LeftDoubleBracket]\)\(1\)\(\ \[RightDoubleBracket]\)\)], 0} + {maxL\/10, 0}\)], "Input"], Cell["definizione delle sezioni", "SmallText"], Cell[BoxData[ \(\(secO[ i_]\)[\[Zeta]_] := {\(asseO[i]\)[\[Zeta]] - maxL\/20\ a\_2[i]\ , \(asseO[i]\)[\[Zeta]] + maxL\/20\ a\_2[i]\ } /. datiO\)], "Input"], Cell["definizione della base adattata", "SmallText"], Cell[BoxData[ \(\(vecOa1[ i_]\)[\[Zeta]_] := {{\(asseO[i]\)[\[Zeta]], \(asseO[i]\)[\[Zeta]] + maxL\/5\ \ a\_1[i]}, {\(asseO[i]\)[\[Zeta] + maxL\/5] + maxL\/15\ \((\(-a\_1[i]\) + a\_2[i]\/2)\), \(asseO[ i]\)[\[Zeta] + maxL\/5]}, {\(asseO[i]\)[\[Zeta] + maxL\/5] + \(\(\(maxL\)\(\ \)\)\/15\) \((\(-a\_1[i]\) - a\_2[i]\/2)\), \(asseO[i]\)[\[Zeta] + maxL\/5]}} /. datiO\)], "Input"], Cell[BoxData[ \(\(vecOa2[ i_]\)[\[Zeta]_] := {{\(asseO[i]\)[\[Zeta]], \(asseO[i]\)[\[Zeta]] + maxL\/5\ \ a\_2[i]}, {\(asseO[i]\)[\[Zeta]] + 1\/5\ maxL\ a\_2[ i] + \(\(\(maxL\)\(\ \)\)\/15\) \((\(-\(1\/2\)\)\ a\_1[i] - a\_2[i])\), \(asseO[i]\)[\[Zeta]] + 1\/5\ maxL\ a\_2[i]}, {\(asseO[i]\)[\[Zeta]] + 1\/5\ maxL\ a\_2[ i] + \(\(\(maxL\)\(\ \)\)\/15\) \((a\_1[i]\/2 - a\_2[i])\), \(asseO[i]\)[\[Zeta]] + 1\/5\ maxL\ a\_2[i]}} /. datiO\)], "Input"], Cell["numero di suddivisioni nel disegno di ciascun tratto", "SmallText"], Cell[BoxData[ \(\(ndiv = 4;\)\)], "Input"], Cell["\<\ disegno dell'asse (la definizione delle estremit\[AGrave] sinistre cambier\ \[AGrave] pi\[UGrave] avanti)\ \>", "SmallText"], Cell[BoxData[ \(\(pltO := Table[Graphics[{AbsoluteThickness[2], Line[{\(asseO[i]\)[0], \(asseO[i]\)[L[i]]}]}], {i, 1, travi}];\)\)], "Input"], Cell[BoxData[ \(\(pltOx := Table[Graphics[{Line[{\(asseO[i]\)[0], \(asseO[i]\)[L[i]]}]}], {i, 1, travi}];\)\)], "Input"], Cell["disegno delle sezioni", "SmallText"], Cell[BoxData[ \(\(pltOs := Table[Table[ Graphics[{Line[\(secO[i]\)[j \(\(\ \)\(L[i]\)\)\/ndiv]]}], {j, 1, ndiv - 1}], {i, 1, travi}] // Flatten;\)\)], "Input"], Cell["disegno della base adattata", "SmallText"], Cell[BoxData[ \(\(pltOa := Graphics[ Table[{Black, AbsoluteThickness[2], Line /@ Join[\(vecOa1[i]\)[L[i]\/2], \(vecOa2[i]\)[ L[i]\/2]]}, {i, 1, travi}]];\)\)], "Input"], Cell[BoxData[ \(\(pltOax := Graphics[ Table[{Black, Line /@ Join[\(vecOa1[i]\)[L[i]\/2], \(vecOa2[i]\)[ L[i]\/2]]}, {i, 1, travi}]];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Disegno della configurazione originaria di ciascuna trave e delle basi \ adattate\ \>", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[pltO, pltOs, pltOa, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.97619 1.34687 0.97619 1.34687 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .97619 .97619 m .02381 .02381 L s .5 Mabswid .69048 .78571 m .78571 .69048 L s .45238 .54762 m .54762 .45238 L s .21429 .30952 m .30952 .21429 L s 0 0 0 r 2 Mabswid .5 .5 m .30952 .30952 L s .40476 .34127 m .30952 .30952 L s .34127 .40476 m .30952 .30952 L s .5 .5 m .69048 .30952 L s .65873 .40476 m .69048 .30952 L s .59524 .34127 m .69048 .30952 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 288}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol3003oOol@Ool000moo`<00?moo`moo`0047oo0`00ogoo3Woo000AOol3003oOol=Ool0019o o`<00?moo`aoo`004goo0`00ogoo2goo000DOol3003oOol:Ool001Eoo`<00?moo`Uoo`005Woo0`00 ogoo27oo000GOol3003oOol7Ool001Qoo`<00?moo`Ioo`006Goo0`00ogoo1Goo000JOol3003oOol4 Ool001]oo`<00?moo`=oo`0077oo0`00ogoo0Woo000MOol3003oOol1Ool001ioo`<00?moo`007goo 0`00oWoo000POol3003mOol0025oo`<00?aoo`008Woo0`00ngoo000SOol3003jOol002Aoo`<00?Uo o`009Goo0`00n7oo000VOol3003gOol002Moo`<00?Ioo`00:7oo0`00mGoo000YOol3003dOol002Yo o`<00?=oo`00:goo0`00lWoo000/Ool3003aOol002eoo`<00?1oo`00;Woo0`00kgoo000_Ool3003^ Ool0031oo`<00>eoo`00Yoo`00=7oo0`00jGoo000e Ool3003XOol003Ioo`<00>Moo`00=goo0`00iWoo000hOol3003UOol003Uoo`<00>Aoo`00>Woo0`00 hgoo000kOol3003ROol003aoo`<001Uoo`03001oogoo0Ool4000eOol4000>Ool30003Ool3001KOol005]o o`8000Aoo`<0011oo`03001oogoo03=oo`03001oogoo00ioo`<000Aoo`8005aoo`00Fgoo0P001Goo 0`00EGoo0`001Goo0P00G7oo001KOol30005Ool3001COol30005Ool3001LOol005aoo`8000Ioo`<0 055oo`<000Ioo`8005eoo`00G7oo0P001goo0`00Cgoo0`001goo0P00GGoo001LOol20008Ool3001= Ool30008Ool2001MOol005aoo`<000Qoo`<004]oo`<000Qoo`<005eoo`00GGoo0P002Goo0`00BGoo 0`002Goo0P00GWoo001MOol2000:Ool30017Ool3000:Ool2001NOol005eoo`<000Yoo`<004Eoo`<0 00Yoo`<005ioo`00GWoo0P002goo0`00@goo0`002goo0P00Ggoo001NOol2000Ool3000kOol3000>Ool2001POol005moo`<000ioo`<003Uoo`<000ioo`<0 061oo`00H7oo0P003goo0`00=goo0`003goo0P00HGoo001POol2000@Ool3000eOol3000@Ool2001Q Ool0061oo`<0011oo`<003=oo`<0011oo`<0065oo`00HGoo00<007ooOol047oo0`00Ool3002?Ool008ioo`@008ioo`00SGoo00<007ooOol00`00SGoo002< Ool00`00Oomoo`02Ool3002Ool30026Ool008Eoo`03001oogoo011oo`<008Eo o`00Q7oo00<007ooOol04Woo0`00Q7oo0023Ool00`00Oomoo`0DOol30023Ool0089oo`03001oogoo 01Ioo`<0089oo`00PGoo00<007ooOol067oo0`00PGoo002MOol30020Ool009ioo`<007moo`00Wgoo 0`00OWoo002POol3001mOol00:5oo`<007aoo`00XWoo0`00Ngoo002SOol3001jOol00:Aoo`<007Uo o`00YGoo0`00N7oo002VOol3001gOol00:Moo`<007Ioo`00Z7oo0`00MGoo002YOol3001dOol00:Yo o`<007=oo`00Zgoo0`00LWoo002/Ool3001aOol00:eoo`<0071oo`00[Woo0`00Kgoo002_Ool3001^ Ool00;1oo`<006eoo`00/Goo0`00K7oo002bOol3001[Ool00;=oo`<006Yoo`00]7oo0`00JGoo002e Ool3001XOol00;Ioo`<006Moo`00]goo0`00IWoo002hOol3001UOol00;Uoo`<006Aoo`00^Woo0`00 Hgoo002kOol3001ROol00;aoo`<0065oo`00_Goo0`00H7oo002nOol3001OOol00;moo`<005ioo`00 `7oo0`00GGoo0031Ool3001LOol00<9oo`<005]oo`00`goo0`00FWoo0034Ool3001IOol005oo`<003aoo`00hWoo0`00>goo003SOol3000jOol00>Aoo`<003Uoo`00iGoo0`00>7oo 003VOol3000gOol00>Moo`<003Ioo`00j7oo0`00=Goo003YOol3000dOol00>Yoo`<003=oo`00jgoo 0`00eoo`<0031oo`00kWoo0`00;goo003_Ool3000^Ool00?1oo`<002eo o`00lGoo0`00;7oo003bOol3000[Ool00?=oo`<002Yoo`00m7oo0`00:Goo003eOol3000XOol00?Io o`<002Moo`00mgoo0`009Woo003hOol3000UOol00?Uoo`<002Aoo`00nWoo0`008goo003kOol3000R Ool00?aoo`<0025oo`00oGoo0`0087oo003nOol3000OOol00?moo`<001ioo`00ogoo0Goo0`007Goo 003oOol2Ool3000LOol00?moo`=oo`<001]oo`00ogoo17oo0`006Woo003oOol5Ool3000IOol00?mo o`Ioo`<001Qoo`00ogoo1goo0`005goo003oOol8Ool3000FOol00?moo`Uoo`<001Eoo`00ogoo2Woo 0`0057oo003oOol;Ool3000COol00?moo`aoo`<0019oo`00ogoo3Goo0`004Goo003oOol>Ool3000@ Ool00?moo`moo`<000moo`00ogoo47oo0`003Woo003oOolAOol3000=Ool00?mooa9oo`<000aoo`00 ogoo4goo0`002goo003oOolDOol3000:Ool00?mooaEoo`<000Uoo`00ogoo5Woo0`0027oo003oOolG Ool30007Ool00?mooaQoo`<000Ioo`00ogoo6Goo00<007ooOol01Goo003oOolQOol00?moob5oo`00 ogoo8Goo003oOolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.724788, -0.724788, 0.002587, \ 0.002587}}] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Distribuzione di forza applicata [", StyleBox["D2", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[TextData[{ "Dati [", StyleBox["D2", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell[BoxData[ \(\(b[i_]\)[\[Zeta]_] := {0, 0}\)], "Input"], Cell[BoxData[ \(\(c[i_]\)[\[Zeta]_] := 0\)], "Input"], Cell[TextData[{ "Se la distribuzione \[EGrave] nulla assegnare il vettore e1 moltiplicato \ per 0 (zero)\n", "(si possono anche usare dei parametri; in tal caso se ne assegni il valore \ nella lista dei dati numerici ", StyleBox["datip(D5)", FontFamily->"Courier New", FontWeight->"Bold"], ")", "\n[ l'uso caratteri script per i parametri rende tutto molto pi\[UGrave] \ leggibile]" }], "SmallText"], Cell[BoxData[ \(\(b[1]\)[\[Zeta]_] := \(-\[ScriptB]\)\ e\_2\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Propriet\[AGrave] di UnitStep nel contesto di questo calcolo (da \ controllare ogni volta)", " [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(Unprotect[UnitStep]\)], "Input"], Cell[BoxData[ \({"UnitStep"}\)], "Output"] }, Open ]], Cell[BoxData[{ \(\(UnitStep[\(-\[ScriptCapitalL]\)] = 0;\)\), "\[IndentingNewLine]", \(\(UnitStep[\(-\(\[ScriptCapitalL]\/2\)\)] = 0;\)\), "\[IndentingNewLine]", \(\(UnitStep[\[ScriptCapitalL]\/2] = 1;\)\), "\[IndentingNewLine]", \(\(UnitStep[\[ScriptCapitalL]] = 1;\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Protect[UnitStep]\)], "Input"], Cell[BoxData[ \({"UnitStep"}\)], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Soluzione generale delle equazioni differenziali di bilancio (bulk)\ \>", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["\<\ Descrittori della tensione (forza normale, taglio e momento) e integrali \ delle equazioni di bilancio\ \>", "Subsection"], Cell[BoxData[ \(\(s[ i_]\)[\[Zeta]_] := \(sN[i]\)[\[Zeta]]\ a\_1[ i] + \(sQ[i]\)[\[Zeta]]\ a\_2[i]\)], "Input"], Cell[BoxData[ \(\(m[i_]\)[\[Zeta]_] := \(sM[i]\)[\[Zeta]]\)], "Input"], Cell[BoxData[ RowBox[{\(eqbilt[i_]\), ":=", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[\(s[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "+", \(\(b[i]\)[\[Zeta]]\)}], ")"}], ".", \(a\_1[i]\)}], "==", "0"}], ",", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[\(s[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "+", \(\(b[i]\)[\[Zeta]]\)}], ")"}], ".", \(a\_2[i]\)}], "==", "0"}], ",", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox[\(sM[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "+", \(\(sQ[i]\)[\[Zeta]]\), "+", \(\(c[i]\)[\[Zeta]]\)}], "==", "0"}]}], "}"}]}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(svar = Flatten[Table[{sN[i], sQ[i], sM[i]}, {i, 1, travi}]]\)], "Input"], Cell[BoxData[ \({sN[1], sQ[1], sM[1]}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(eqbil = Flatten[Simplify[Table[eqbilt[i], {i, 1, travi}]]];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(bulksolC = \(DSolve[eqbil, svar, \[Zeta], DSolveConstants \[Rule] \[ScriptCapitalC]]\)\[LeftDoubleBracket]1\ \[RightDoubleBracket]\)], "Input"], Cell[BoxData[ \({sN[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + \ \[ScriptCapitalC][1]], sQ[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + \ \[ScriptCapitalC][2]], sM[1] \[Rule] Function[{\[Zeta]}, \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) - \[Zeta]\ \ \[ScriptCapitalC][2] + \[ScriptCapitalC][3]]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Cambiamento delle costanti di integrazione", "Subsection"], Cell["\<\ Viene costruita la lista cNQMO delle costanti di integrazione delle equazioni \ di bilancio. La lista cNQM delle costanti di integrazione presenti nelle condizioni al \ bordo, costruita pi\[UGrave] avanti, \[EGrave] in generale contenuta in \ questa.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(cClist = Table[\[ScriptCapitalC][i], {i, 1, 3 travi}]\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalC][1], \[ScriptCapitalC][2], \[ScriptCapitalC][ 3]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cNQM = Table[{sNo[i], sQo[i], sMo[i]}, {i, 1, travi}] // Flatten\)], "Input"], Cell[BoxData[ \({sNo[1], sQo[1], sMo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Table[{\(sN[i]\)[0] == sNo[i], \(sQ[i]\)[0] == sQo[i], \(sM[i]\)[0] == sMo[i]} /. bulksolC, {i, 1, travi}] // Simplify\) // Flatten\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalC][1] == sNo[1], \[ScriptCapitalC][2] == sQo[1], \[ScriptCapitalC][3] == sMo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(fromCtoNQM = \(Solve[\(Table[{\(sN[i]\)[0] == sNo[i], \(sQ[i]\)[0] == \ sQo[i], \(sM[i]\)[0] == sMo[i]} /. bulksolC, {i, 1, travi}] // Simplify\) // \ Flatten, cClist]\)\_\(\(\[LeftDoubleBracket]\)\(1\)\(\[RightDoubleBracket]\)\)\ \)], "Input"], Cell[BoxData[ \({\[ScriptCapitalC][1] \[Rule] sNo[1], \[ScriptCapitalC][2] \[Rule] sQo[1], \[ScriptCapitalC][3] \[Rule] sMo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(bulksol = bulksolC /. fromCtoNQM\)], "Input"], Cell[BoxData[ \({sN[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + sNo[1]], sQ[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + sQo[1]], sM[1] \[Rule] Function[{\[Zeta]}, \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) - \[Zeta]\ \ sQo[1] + sMo[1]]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Equazioni di bilancio e integrali (sintesi)", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Table[eqbilt[i], {i, 1, travi}] // Simplify\) // Flatten\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ { RowBox[{ RowBox[{\(\[ScriptB]\/\@2\), "+", RowBox[{ SuperscriptBox[\(sN[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "==", "0"}]}, { RowBox[{ RowBox[{\(\[ScriptB]\/\@2\), "+", RowBox[{ SuperscriptBox[\(sQ[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "==", "0"}]}, { RowBox[{ RowBox[{\(\(sQ[1]\)[\[Zeta]]\), "+", RowBox[{ SuperscriptBox[\(sM[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "==", "0"}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB]], Derivative[ 1][ sN[ 1]][ \[Zeta]]], 0], Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB]], Derivative[ 1][ sQ[ 1]][ \[Zeta]]], 0], Equal[ Plus[ sQ[ 1][ \[Zeta]], Derivative[ 1][ sM[ 1]][ \[Zeta]]], 0]}], Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Table[\(svar\[LeftDoubleBracket] i\[RightDoubleBracket]\)[\[Zeta]] == \((\(svar\ \[LeftDoubleBracket]i\[RightDoubleBracket]\)[\[Zeta]] /. bulksolC)\), {i, 1, Length[svar]}] // Simplify\) // Flatten\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(\[ScriptB]\ \[Zeta]\)\/\@2 + \(sN[ 1]\)[\[Zeta]] == \[ScriptCapitalC][1]\)}, {\(\(\[ScriptB]\ \[Zeta]\)\/\@2 + \(sQ[ 1]\)[\[Zeta]] == \[ScriptCapitalC][2]\)}, {\(\[Zeta]\ \[ScriptCapitalC][2] + \(sM[ 1]\)[\[Zeta]] == \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) + \ \[ScriptCapitalC][3]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB], \[Zeta]], sN[ 1][ \[Zeta]]], \[ScriptCapitalC][ 1]], Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB], \[Zeta]], sQ[ 1][ \[Zeta]]], \[ScriptCapitalC][ 2]], Equal[ Plus[ Times[ \[Zeta], \[ScriptCapitalC][ 2]], sM[ 1][ \[Zeta]]], Plus[ Times[ Rational[ 1, 2], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[Zeta], 2]], \[ScriptCapitalC][ 3]]]}], Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Table[\(svar\[LeftDoubleBracket] i\[RightDoubleBracket]\)[\[Zeta]] == \((\(svar\ \[LeftDoubleBracket]i\[RightDoubleBracket]\)[\[Zeta]] /. bulksol)\), {i, 1, Length[svar]}] // Simplify\) // Flatten\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(\[ScriptB]\ \[Zeta]\)\/\@2 + \(sN[1]\)[\[Zeta]] == sNo[1]\)}, {\(\(\[ScriptB]\ \[Zeta]\)\/\@2 + \(sQ[1]\)[\[Zeta]] == sQo[1]\)}, {\(\[Zeta]\ sQo[1] + \(sM[ 1]\)[\[Zeta]] == \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) + sMo[1]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB], \[Zeta]], sN[ 1][ \[Zeta]]], sNo[ 1]], Equal[ Plus[ Times[ Power[ 2, Rational[ -1, 2]], \[ScriptB], \[Zeta]], sQ[ 1][ \[Zeta]]], sQo[ 1]], Equal[ Plus[ Times[ \[Zeta], sQo[ 1]], sM[ 1][ \[Zeta]]], Plus[ Times[ Rational[ 1, 2], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[Zeta], 2]], sMo[ 1]]]}], Editable->False]], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Definizioni di spostamenti e forze al bordo", "Section"], Cell[BoxData[ \(meno = "\<-\>"; pi\[UGrave] = "\<+\>";\)], "Input"], Cell["\<\ Spostamento, atti di moto e forze al bordo come combinazioni lineari dei \ vettori delle basi adattate al bordo {d,n}\ \>", "SmallText"], Cell[BoxData[{ \(\(\(ub[i_]\)[ bd_] := \(ub\_d[i]\)[bd]\ \(d[i]\)[bd] + \(ub\_n[i]\)[bd]\ \(n[i]\)[ bd];\)\), "\n", \(\(\(wb[i_]\)[ bd_] := \(wb\_d[i]\)[bd]\ \(d[i]\)[bd] + \(wb\_n[i]\)[bd]\ \(n[i]\)[ bd];\)\), "\n", \(\(\(sb[i_]\)[ bd_] := \(sb\_d[i]\)[bd]\ \(d[i]\)[bd] + \(sb\_n[i]\)[bd]\ \(n[i]\)[ bd];\)\)}], "Input"], Cell["Lista delle componenti dello spostamento al bordo", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(spbd = Table[\({\(ub\_d[i]\)[#], \(ub\_n[i]\)[#], \(\[Theta]b[ i]\)[#]} &\)\ /@ \ {pi\[UGrave], meno}, {i, 1, travi}] // Flatten\)], "Input"], Cell[BoxData[ \({\(ub\_d[1]\)["+"], \(ub\_n[1]\)["+"], \(\[Theta]b[1]\)[ "+"], \(ub\_d[1]\)["-"], \(ub\_n[1]\)["-"], \(\[Theta]b[1]\)[ "-"]}\)], "Output"] }, Open ]], Cell["Lista delle componenti dell'atto di moto al bordo", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(ambd = Table[\({\(wb\_d[i]\)[#], \(wb\_n[i]\)[#], \(\[Omega]b[ i]\)[#]} &\)\ /@ \ {pi\[UGrave], meno}, {i, 1, travi}] // Flatten\)], "Input"], Cell[BoxData[ \({\(wb\_d[1]\)["+"], \(wb\_n[1]\)["+"], \(\[Omega]b[1]\)[ "+"], \(wb\_d[1]\)["-"], \(wb\_n[1]\)["-"], \(\[Omega]b[1]\)[ "-"]}\)], "Output"] }, Open ]], Cell["Lista delle componenti delle forze al bordo", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(fbd = Table[\({\(sb\_d[i]\)[#], \(sb\_n[i]\)[#], \(mb[ i]\)[#]} &\)\ /@ \ {pi\[UGrave], meno}, {i, 1, travi}] // Flatten\)], "Input"], Cell[BoxData[ \({\(sb\_d[1]\)["+"], \(sb\_n[1]\)["+"], \(mb[1]\)["+"], \(sb\_d[1]\)[ "-"], \(sb\_n[1]\)["-"], \(mb[1]\)["-"]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Basi adattate al bordo e vincoli [", StyleBox["D3", FontColor->RGBColor[0, 0, 1]], "]" }], "Section"], Cell[CellGroupData[{ Cell["Descrizioni di vincoli standard", "Subsection"], Cell[BoxData[ \(\(carrelloV[trv_]\)[bnd_] := \(ub[trv]\)[bnd] . \(n[trv]\)[bnd] == 0\)], "Input"], Cell[BoxData[ \(\(cernieraV[trv_]\)[ bnd_] := {\(ub[trv]\)[bnd] . a\_1[trv] == 0, \(ub[trv]\)[bnd] . a\_2[trv] == 0}\)], "Input"], Cell[BoxData[ \(\(pernoV[trv1_, trv2_]\)[bnd1_, bnd2_] := {\((\(ub[trv2]\)[bnd2] - \(ub[trv1]\)[bnd1])\) . a\_1[trv2] == 0, \((\(ub[trv2]\)[bnd2] - \(ub[trv1]\)[bnd1])\) . a\_2[trv2] == 0}\)], "Input"], Cell[BoxData[ \(\(saldaturaV[trv1_, trv2_]\)[bnd1_, bnd2_] := {\((\(ub[trv2]\)[bnd2] - \(ub[trv1]\)[bnd1])\) . a\_1[trv2] == 0, \((\(ub[trv2]\)[bnd2] - \(ub[trv1]\)[bnd1])\) . a\_2[trv2] == 0, \(\[Theta]b[trv2]\)[bnd2] - \(\[Theta]b[trv1]\)[bnd1] \[Equal] 0}\)], "Input"], Cell[BoxData[ \(\(incastroV[trv_]\)[ bnd_] := {\(ub[trv]\)[bnd] . a\_1[trv] == 0, \(ub[trv]\)[bnd] . a\_2[trv] == 0, \(\[Theta]b[trv]\)[bnd] == 0}\)], "Input"], Cell["\<\ Per ogni nuova definizione, anche occasionale, occorre dare la corrispondente \ definizione della figura\ \>", "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Dati [", StyleBox["D3", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell["\<\ n vettore normale al piano di scorrimento di un carrello; d vettore tangenziale; {d, n} base ortonormale orientata come {e1, e2}\ \>", "SmallText"], Cell[BoxData[ \(\(Clear[d, n];\)\)], "Input"], Cell[BoxData[{ \(\(\(d[i_]\)[bd_] := e\_1;\)\), "\n", \(\(\(n[i_]\)[bd_] := e\_2;\)\)}], "Input"], Cell["\<\ Si assume che {d,n} siano identici a {e1,e2} a meno di una esplicita diversa \ definizione\ \>", "SmallText"], Cell[BoxData[{ \(\(\(d[1]\)[meno] = \(-e\_1\);\)\), "\[IndentingNewLine]", \(\(\(n[1]\)[meno] = \(-e\_2\);\)\)}], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell["\<\ Vincoli in forma scalare. Non usare esplicitamente le componenti ! Si \ pregiudicherebbe il meccanismo di sostituzione utilizzato nel calcolo della \ soluzione in termini di spostamento dalle equazioni di vincolo, oltre che \ incorrere pi\[UGrave] facilmente in errore. Utilizzare SEMPRE vincoli \ definiti secondo il modello dei vincoli standard, anche per definizioni \ occasionali. Ricordare di dare una definizione anche della figura del vincolo \ per la visualizzazione.\ \>", "SmallText"], Cell[BoxData[ \(vincoliDef := {\(incastro[1]\)[pi\[UGrave]], \(carrello[1]\)[ meno]}\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[ \(vincoli := \(Block[{carrello = carrelloV, cerniera = cernieraV, perno = pernoV, incastro = incastroV, saldatura = saldaturaV}, vincoliDef] // Flatten\) // Simplify\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(vincoli\)], "Input"], Cell[BoxData[ \({\(\(ub\_d[1]\)["+"] + \(ub\_n[1]\)["+"]\)\/\@2 == 0, \(\(ub\_d[1]\)["+"] - \(ub\_n[1]\)["+"]\)\/\@2 == 0, \(\[Theta]b[1]\)["+"] == 0, \(ub\_n[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell["Condizioni di vincolo come regole di sostituzione", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(vsp = \(Solve[\ vincoli, spbd]\)\[LeftDoubleBracket]1\[RightDoubleBracket] // Sort\)], "Input"], Cell[BoxData[ \({\(\[Theta]b[1]\)["+"] \[Rule] 0, \(ub\_d[1]\)["+"] \[Rule] 0, \(ub\_n[1]\)["-"] \[Rule] 0, \(ub\_n[1]\)["+"] \[Rule] 0}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Definizioni per la visualizzazione", "Subsection"], Cell["Condizioni di vincolo sui collegamenti tra le travi", "SmallText"], Cell[BoxData[ \(Clear[coll]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(vincoliDef\)], "Input"], Cell[BoxData[ \({\(incastro[1]\)["+"], \(carrello[1]\)["-"]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Complement[ vincoliDef /. {carrello \[Rule] \((\((Null\ &)\)\ &)\), incastro \[Rule] \((\((Null\ &)\)\ &)\), cerniera \[Rule] \((\((Null\ &)\)\ &)\), perno \[Rule] coll, saldatura \[Rule] coll}, {Null}]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell["\<\ Calcolo della posizione della estremit\[AGrave] sinistra indotta dalla \ presenza di vincoli di collegamento tra le tarvi\ \>", "SmallText"], Cell[BoxData[ \(Clear[org]\)], "Input"], Cell[BoxData[ \(\(org[1] = {0, 0};\)\)], "Input"], Cell[BoxData[ \(\(coll[i_, j_]\)[bi_, bj_] := Block[{p = Sort[{{i, bi}, {j, bj}}, #1\_\(\(\[LeftDoubleBracket]\)\(1\)\(\ \[RightDoubleBracket]\)\) < #2\_\(\(\[LeftDoubleBracket]\)\(1\)\(\ \[RightDoubleBracket]\)\)\ &]}, Block[{ix = p\_\(\(\[LeftDoubleBracket]\)\(1, \ 1\)\(\[RightDoubleBracket]\)\), jx = p\_\(\(\[LeftDoubleBracket]\)\(2, 1\)\(\[RightDoubleBracket]\ \)\), bix = p\_\(\(\[LeftDoubleBracket]\)\(1, 2\)\(\[RightDoubleBracket]\)\), bjx = p\_\(\(\[LeftDoubleBracket]\)\(2, \ 2\)\(\[RightDoubleBracket]\)\)}, \[IndentingNewLine]Switch[{bix, bjx}, \[IndentingNewLine]{pi\[UGrave], meno}, {org[jx] = Evaluate[ org[ix] + a\_1[ix] L[ix] /. datiO]}, \[IndentingNewLine]{pi\[UGrave], pi\[UGrave]}, {org[jx] = Evaluate[ org[ix] + a\_1[ix] L[ix] - a\_1[jx] L[jx] /. datiO]}, \[IndentingNewLine]{meno, meno}, {org[jx] = Evaluate[org[ix] /. datiO]}, \[IndentingNewLine]{meno, pi\[UGrave]}, {org[jx] = Evaluate[org[ix] - a\_1[jx] L[jx] /. datiO]}]]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{carrello = \((\((Null\ &)\)\ &)\), incastro = \((\((Null\ &)\)\ &)\), cerniera = \((\((Null\ &)\)\ &)\), perno = coll, saldatura = coll}, Complement[vincoliDef, {Null}]]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Definition[org]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(org[1] = {0, 0}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ org], Editable->False]], "Output"] }, Open ]], Cell["\<\ Definizione delle funzioni che generano le figure dei vincoli\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(vincoliDef\)], "Input"], Cell[BoxData[ \({\(incastro[1]\)["+"], \(carrello[1]\)["-"]}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(vincoliFig := Block[{carrello = carrelloFig, cerniera = cernieraFig, perno = pernoFig, saldatura = saldaturaFig, incastro = incastroFig}, vincoliDef];\)\)], "Input"], Cell[BoxData[ \(vincolibFig := Block[{carrello = crosshairFig, cerniera = crosshairFig, perno = crosshairFig, saldatura = crosshairFig, incastro = crosshairFig}, vincoliDef]\)], "Input"], Cell["definizione delle estrremit\[AGrave] dell'asse", "SmallText"], Cell[BoxData[ \(\(asseOb[i_]\)[meno] := \(asseO[i]\)[0]\)], "Input"], Cell[BoxData[ \(\(asseOb[i_]\)[pi\[UGrave]] := \(asseO[i]\)[L[i]]\)], "Input"], Cell[BoxData[ \(\(crosshairFig[i_]\)\ [bd_] := Graphics[{AbsoluteThickness[1], Line[{\(asseOb[i]\)[bd] - \(d[i]\)[bd] maxL\/12, \(asseOb[i]\)[ bd] + \(d[i]\)[bd] maxL\/12}], Line[{\(asseOb[i]\)[bd] - \(n[i]\)[bd] maxL\/8, \(asseOb[i]\)[ bd] + \(n[i]\)[bd] maxL\/8}], Circle[\(asseOb[i]\)[bd], 0.04]}]\)], "Input"], Cell[BoxData[ \(\(crosshairFig[i_, j_]\)\ [bd_, bdj_] := Graphics[{AbsoluteThickness[1], Line[{\(asseOb[i]\)[bd] - \(d[i]\)[bd] maxL\/12, \(asseOb[i]\)[ bd] + \(d[i]\)[bd] maxL\/12}], Line[{\(asseOb[i]\)[bd] - \(n[i]\)[bd] maxL\/8, \(asseOb[i]\)[ bd] + \(n[i]\)[bd] maxL\/8}], Circle[\(asseOb[i]\)[bd], 0.04]}]\)], "Input"], Cell[BoxData[ \(\(incastroFig[i_]\)\ [bd_] := Graphics[{AbsoluteThickness[2], Line[{\(asseOb[i]\)[bd] - a\_2[i] maxL\/10, \(asseOb[i]\)[bd] + a\_2[i] maxL\/10}]}]\)], "Input"], Cell[BoxData[ \(\(carrelloFig[i_]\)\ [bd_] := Graphics[{AbsoluteThickness[2], Line[{\(asseOb[i]\)[ bd], \(asseOb[i]\)[bd] - \((\(d[i]\)[bd] + \(n[i]\)[bd])\) maxL\/10, \(asseOb[i]\)[ bd] + \((\(d[i]\)[bd] - \(n[i]\)[bd])\) maxL\/10, \(asseOb[ i]\)[bd]}], Line[{\(asseOb[i]\)[bd] - \((\(d[i]\)[bd] + \(n[i]\)[bd])\) maxL\/10 - \(n[i]\)[bd] maxL\/50, \(asseOb[i]\)[ bd] + \((\(d[i]\)[bd] - \(n[i]\)[bd])\) maxL\/10 - \(n[i]\)[bd] maxL\/50}], {GrayLevel[1], Disk[\(asseOb[i]\)[bd], 0.04]}, Circle[\(asseOb[i]\)[bd], 0.04]}]\)], "Input"], Cell[BoxData[ \(\(cernieraFig[i_]\)\ [bd_] := Graphics[{AbsoluteThickness[2], Line[{\(asseOb[i]\)[ bd], \(asseOb[i]\)[bd] - \((\(d[i]\)[bd] + \(n[i]\)[bd])\) maxL\/10, \(asseOb[i]\)[ bd] + \((\(d[i]\)[bd] - \(n[i]\)[bd])\) maxL\/10, \(asseOb[ i]\)[bd]}], {GrayLevel[1], Disk[\(asseOb[i]\)[bd], 0.04]}, Circle[\(asseOb[i]\)[bd], 0.04]}]\)], "Input"], Cell[BoxData[ \(\(pernoFig[i_, j_]\)\ [bd_, bdj_] := Graphics[{AbsoluteThickness[2], {GrayLevel[1], Disk[\(asseOb[i]\)[bd], 0.04]}, Circle[\(asseOb[i]\)[bd], 0.04]}]\)], "Input"], Cell[BoxData[ \(\(saldaturaFig[i_, j_]\)\ [bd_, bdj_] := Graphics[{AbsoluteThickness[2], Disk[\(asseOb[i]\)[bd], 0.02]}]\)], "Input"], Cell[BoxData[ \(\(pltOv := vincoliFig;\)\)], "Input"], Cell[BoxData[ \(\(pltObv := vincolibFig;\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Disegno della configurazione originaria con i vincoli", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[pltO, pltOa, pltObv, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.09537 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.88536 1.08996 0.933046 1.08996 [ [ 0 0 0 0 ] [ 1 1.09537 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.09537 L 0 1.09537 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .88536 .93305 m .11464 .16233 L s 0 0 0 r .5 .54769 m .34586 .39354 L s .42293 .41923 m .34586 .39354 L s .37155 .47061 m .34586 .39354 L s .5 .54769 m .65414 .39354 L s .62845 .47061 m .65414 .39354 L s .57707 .41923 m .65414 .39354 L s 0 g 1 Mabswid .02381 .16233 m .20547 .16233 L s .11464 .02608 m .11464 .29857 L s newpath .11464 .16233 .0436 0 365.73 arc s .97619 .93305 m .79453 .93305 L s .88536 1.06929 m .88536 .7968 L s newpath .88536 .93305 .0436 0 365.73 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 315.438}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHga000`40O003h00Oogoo8Goo003oOolQ Ool00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol0021oo`03001o ogoo0?eoo`0087oo00<007ooOol0oGoo000POol00`00Oomoo`3mOol0021oo`03001oogoo0?eoo`00 87oo00<007ooOol0oGoo000POol00`00Oomoo`3mOol0021oo`03001oogoo0?eoo`0087oo00<007oo Ool0oGoo000POol00`00Oomoo`3mOol0021oo`03001oogoo0?eoo`0087oo00<007ooOol0oGoo000P Ool00`00Oomoo`3mOol0021oo`03001oogoo0?eoo`0087oo00<007ooOol0oGoo000POol00`00Oomo o`3mOol0021oo`03001oogoo0?eoo`0087oo00<007ooOol0oGoo000POol00`00Oomoo`3mOol0021o o`03001oogoo0?eoo`0087oo00<007ooOol0oGoo000POol00`00Oomoo`3mOol0021oo`03001oogoo 0?eoo`0087oo00<007ooOol0oGoo000POol00`00Oomoo`3mOol0021oo`03001oogoo0?eoo`0087oo 00<007ooOol0oGoo000NOol5003mOol001aoo`80009oo`03001oogoo00800?]oo`006Woo0P0017oo 00<007ooOol00Woo0P00nGoo000HOol20006Ool00`00Oomoo`04Ool2003gOol001Moo`03001oogoo 00Ioo`03001oogoo00Ioo`03001oogoo0?Aoo`005Woo00<007ooOol01goo00<007ooOol01goo00<0 07ooOol0lgoo000EOol00`00Oomoo`08Ool00`00Oomoo`07Ool00`00Oomoo`3cOol001Eoo`03001o ogoo00Qoo`03001oogoo00Qoo`03001oogoo0?9oo`005Goo00<007ooOol027oo00<007ooOol027oo 00<007ooOol0lWoo000DOol00`00Oomoo`09Ool00`00Oomoo`09Ool00`00Oomoo`3aOol001Aoo`03 001oogoo00Uoo`03001oogoo00Uoo`03001oogoo0?5oo`0057oo00<007ooOol02Goo00<007ooOol0 2Woo00<007ooOol0l7oo000DOol00`00Oomoo`09Ool00`00Oomoo`0:Ool00`00Oomoo`3`Ool000Io ocD00>Eoo`0057oo00<007ooOol02Goo0`002Woo00<007ooOol0l7oo000DOol00`00Oomoo`09Ool4 0009Ool00`00Oomoo`3`Ool001Aoo`03001oogoo00Uoo`03001oo`00008000Qoo`03001oogoo0?1o o`005Goo00<007ooOol027oo00<007ooOol00`001Woo00<007ooOol0lGoo000EOol00`00Oomoo`08 Ool01000Oomoogoo0`001Goo00<007ooOol0lGoo000FOol00`00Oomoo`07Ool00`00Oomoo`02Ool3 0003Ool00`00Oomoo`3bOol001Ioo`03001oogoo00Moo`03001oogoo00=oo`<0009oo`03001oogoo 0?9oo`005goo00<007ooOol01Woo00<007ooOol017oo1000mGoo000HOol00`00Oomoo`05Ool00`00 Oomoo`05Ool3003eOol001Uoo`03001oogoo00Aoo`03001oogoo00Aoo`D00?Aoo`006Woo0`000goo 00<007ooOol00Woo0P000goo0`00lgoo000MOol80006Ool3003bOol0021oo`03001oogoo00Uoo`<0 0?5oo`0087oo00<007ooOol02Woo0`00l7oo000POol00`00Oomoo`0;Ool3003_Ool0021oo`03001o ogoo00aoo`<00>ioo`0087oo00<007ooOol03Goo0`00kGoo000POol00`00Oomoo`0>Ool3003/Ool0 021oo`03001oogoo00moo`<00>]oo`0087oo00<007ooOol047oo0`00jWoo000POol00`00Oomoo`0A Ool3003YOol0021oo`03001oogoo019oo`<00>Qoo`0087oo00<007ooOol04goo0`00igoo000POol0 0`00Oomoo`0DOol3003VOol0021oo`03001oogoo01Eoo`<00>Eoo`0087oo00<007ooOol05Woo0`00 i7oo000POol00`00Oomoo`0GOol3003SOol0021oo`03001oogoo01Qoo`<00>9oo`0087oo00<007oo Ool06Goo0`00hGoo000POol00`00Oomoo`0JOol3003POol0021oo`03001oogoo01]oo`<00=moo`00 87oo00<007ooOol077oo0`00gWoo000POol00`00Oomoo`0MOol3003MOol0021oo`03001oogoo01io o`<00=aoo`0087oo00<007ooOol07goo0`00fgoo000POol00`00Oomoo`0POol3003JOol0021oo`03 001oogoo025oo`<00=Uoo`0087oo00<007ooOol08Woo0`00f7oo000POol00`00Oomoo`0SOol3003G Ool004Moo`<00=Ioo`00B7oo0`00eGoo0019Ool3003DOol004Yoo`<00==oo`00Bgoo0`00dWoo001< Ool3003AOol004eoo`<00=1oo`00CWoo0`00cgoo001?Ool3003>Ool0051oo`<001oo`<0 01]oo`03001oogoo01moo`00hGoo0`006Woo00<007ooOol07goo003ROol3000IOol00`00Oomoo`0O Ool00>=oo`<001Qoo`03001oogoo01moo`00i7oo0`005goo00<007ooOol07goo003UOol3000FOol0 0`00Oomoo`0OOol00>Ioo`<001Eoo`03001oogoo01moo`00igoo0`0057oo00<007ooOol07goo003X Ool3000COol00`00Oomoo`0OOol00>Uoo`<0019oo`03001oogoo01moo`00jWoo0`004Goo00<007oo Ool07goo003[Ool3000@Ool00`00Oomoo`0OOol00>aoo`<000moo`03001oogoo01moo`00kGoo0`00 3Woo00<007ooOol07goo003^Ool3000=Ool00`00Oomoo`0OOol00>moo`<000aoo`03001oogoo01mo o`00l7oo0`002Goo100087oo003aOol30005Ool30002Ool01000Ool000007Woo003bOol30002Ool2 0005Ool01000Oomoogoo0P0077oo003cOol40007Ool00`00Oomoo`03Ool2000JOol00?Aoo`<000Mo o`03001oogoo00Eoo`03001oogoo01Moo`00m7oo10001Woo00<007ooOol01Woo00<007ooOol05Woo 003cOol00`00Oomoo`030005Ool00`00Oomoo`07Ool00`00Oomoo`0EOol00?9oo`03001oogoo009o o`<000Aoo`03001oogoo00Qoo`03001oogoo01Aoo`00lWoo00<007ooOol00goo0`000goo00<007oo Ool027oo00<007ooOol057oo003aOol00`00Oomoo`05Ool30002Ool00`00Oomoo`09Ool00`00Oomo o`0COol00?5oo`03001oogoo00Ioo`<00003Ool007oo00Yoo`03001oogoo01=oo`00lGoo00<007oo Ool01goo10002goo00<007ooOol04goo003aOol00`00Oomoo`08Ool3000;Ool00`00Oomoo`0COol0 0>AoocD000Moo`00lGoo00<007ooOol02Woo00<007ooOol02Goo00<007ooOol04goo003aOol00`00 Oomoo`0:Ool00`00Oomoo`09Ool00`00Oomoo`0COol00?5oo`03001oogoo00Yoo`03001oogoo00Uo o`03001oogoo01=oo`00lWoo00<007ooOol02Goo00<007ooOol027oo00<007ooOol057oo003bOol0 0`00Oomoo`09Ool00`00Oomoo`08Ool00`00Oomoo`0DOol00?=oo`03001oogoo00Qoo`03001oogoo 00Moo`03001oogoo01Eoo`00lgoo00<007ooOol027oo00<007ooOol01goo00<007ooOol05Goo003d Ool00`00Oomoo`07Ool00`00Oomoo`06Ool00`00Oomoo`0FOol00?Eoo`03001oogoo00Ioo`03001o ogoo00Eoo`03001oogoo01Moo`00mWoo00<007ooOol01Goo00<007ooOol00goo0P006Woo003gOol3 0004Ool00`00Oomoo`02Ool00`00Oomoo`0JOol00?Yoo`T001eoo`00oWoo00<007ooOol07goo003n Ool00`00Oomoo`0OOol00?ioo`03001oogoo01moo`00oWoo00<007ooOol07goo003nOol00`00Oomo o`0OOol00?ioo`03001oogoo01moo`00oWoo00<007ooOol07goo003nOol00`00Oomoo`0OOol00?io o`03001oogoo01moo`00oWoo00<007ooOol07goo003nOol00`00Oomoo`0OOol00?ioo`03001oogoo 01moo`00oWoo00<007ooOol07goo003nOol00`00Oomoo`0OOol00?ioo`03001oogoo01moo`00oWoo 00<007ooOol07goo003nOol00`00Oomoo`0OOol00?ioo`03001oogoo01moo`00oWoo00<007ooOol0 7goo003nOol00`00Oomoo`0OOol00?ioo`03001oogoo01moo`00oWoo00<007ooOol07goo003nOol0 0`00Oomoo`0OOol00?ioo`03001oogoo01moo`00oWoo00<007ooOol07goo003nOol00`00Oomoo`0O Ool00?ioo`03001oogoo01moo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol0 0?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {314.438, 0}} -> {-0.812291, -0.856148, \ 0.00319677, 0.00319677}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[pltO, pltOa, pltOv, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.02278 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.867696 1.08494 0.868239 1.08494 [ [ 0 0 0 0 ] [ 1 1.02278 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.02278 L 0 1.02278 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .8677 .86824 m .10053 .10107 L s 0 0 0 r .48411 .48465 m .33068 .33122 L s .40739 .35679 m .33068 .33122 L s .35625 .40794 m .33068 .33122 L s .48411 .48465 m .63755 .33122 L s .61197 .40794 m .63755 .33122 L s .56083 .35679 m .63755 .33122 L s 0 g .02381 .17779 m .17724 .02435 L s .8677 .86824 m .97619 .97673 L .7592 .97673 L .8677 .86824 L s .97619 .99843 m .7592 .99843 L s 1 g .8677 .86824 m .8677 .86824 .0434 0 365.73 arc F 0 g newpath .8677 .86824 .0434 0 365.73 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 294.5}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgeoo`00;goo0`00kWoo000^Ool3003_Ool002eoo`<00?1oo`00;7oo0`00lGoo000[ Ool3003bOol002Yoo`<00?=oo`00:Goo0`00m7oo000XOol3003eOol002Moo`<00?Ioo`009Woo0`00 mgoo000UOol3003hOol002Aoo`<00?Uoo`008goo0`00nWoo000ROol3003kOol0025oo`<00?aoo`00 87oo0`00oGoo000OOol3003nOol001ioo`<00?moo`007Goo0`00ogoo0Goo000LOol3003oOol2Ool0 01]oo`<00?moo`=oo`006Woo1@00ogoo0Woo000IOol3000017oo00000000ogoo0Goo000HOol30003 Ool3003oOol001Moo`<000Eoo`<00?ioo`005Woo0`001goo0`00oGoo000EOol30009Ool3003lOol0 01Aoo`<000]oo`<00?]oo`004goo0`003Goo0`00nWoo000BOol3000?Ool3003iOol0015oo`<0015o o`<00?Qoo`0047oo0`004goo0`00mgoo000?Ool3000EOol3003fOol000ioo`<001Moo`<00?Eoo`00 3Goo0`006Goo0`00m7oo000moo`001goo0`009Goo0`00kWoo0006 Ool3000WOol3003]Ool000Eoo`<002Uoo`<00>aoo`001Woo00<007ooOol0:Goo0`00jgoo000cOol3 003ZOol003Aoo`<00>Uoo`00=Goo0`00j7oo000fOol3003WOol003Moo`<00>Ioo`00>7oo0`00iGoo 000iOol3003TOol003Yoo`<00>=oo`00>goo0`00hWoo000lOol3003QOol003eoo`<00>1oo`00?Woo 0`00ggoo000oOol3003NOol0041oo`<00=eoo`00@Goo0`00g7oo0012Ool3003KOol004=oo`<00=Yo o`00A7oo0`00fGoo0015Ool3003HOol004Ioo`<00=Moo`00Agoo0`00eWoo0018Ool3003EOol004Uo o`<00=Aoo`00BWoo0`00dgoo001;Ool3003BOol004aoo`<00=5oo`00CGoo0`00d7oo001>Ool3003? Ool004moo`<00goo0`001Woo0`00 K7oo001ROol30006Ool3000iOol30007Ool2001]Ool006=oo`8000Moo`<003Moo`<000Qoo`8006eo o`00Hgoo0P0027oo0`00=Goo0`0027oo0`00KGoo001SOol30008Ool3000cOol30009Ool2001^Ool0 06Aoo`8000Uoo`<0035oo`<000Yoo`8006ioo`00I7oo0`002Goo0`00;goo0`002Woo0`00KWoo001U Ool2000:Ool3000]Ool3000;Ool2001_Ool006Eoo`8000]oo`<002]oo`<000aoo`8006moo`00IGoo 0`002goo0`00:Goo0`0037oo0`00Kgoo001VOol00`00Oomoo`0;Ool3000WOol3000>Ool00`00Oomo o`1^Ool007Eoo`<002Eoo`<0081oo`00MWoo0`008goo0`00PGoo001gOol3000QOol30022Ool007Qo o`<001moo`<008=oo`00NGoo0`007Goo0`00Q7oo001jOol3000KOol30025Ool007]oo`<001Uoo`<0 08Ioo`00O7oo0`005goo0`00Qgoo001mOol3000EOol30028Ool007ioo`<001=oo`<008Uoo`00Ogoo 0`004Goo0`00RWoo0020Ool3000?Ool3002;Ool0085oo`<000eoo`<008aoo`00PWoo0`002goo0`00 SGoo0023Ool30009Ool3002>Ool008Aoo`<000Moo`<008moo`00QGoo0`001Goo0`00T7oo0026Ool3 0003Ool3002AOol008Moo`<00004Ool00000002BOol008Qoo`D009=oo`00RGoo1000Tgoo002:Ool4 002BOol008aoo`<0095oo`00SGoo0`00T7oo002>Ool3002?Ool008moo`<008ioo`00T7oo0`00SGoo 002AOol30021oo`<003eoo`00hGoo0`00?7oo003ROol3000k Ool00>=oo`<003Yoo`00i7oo0`00>Goo003UOol3000hOol00>Ioo`<003Moo`00igoo0`00=Woo003X Ool3000eOol00>Uoo`<003Aoo`00jWoo0`00aoo`<000=oo`d0025oo`00 kGoo0`0000=oo`0000003P007goo003^Ool5000;Ool4000NOol00>moo`<000ioo`<001eoo`00kgoo 0P0047oo0P007Goo003^Ool2000BOol2000LOol00>eoo`<001=oo`03001oogoo01Yoo`00kGoo0P00 57oo0P006goo003/Ool2000FOol00`00Oomoo`0IOol00>aoo`03001oogoo01Eoo`8001Yoo`00jgoo 0P005goo0P006Woo003[Ool2000GOol2000JOol00>]oo`8001Moo`8001Yoo`00jgoo0P005goo0P00 6Woo003/Ool00`00Oomoo`0EOol2000JOol00>aoo`8001Ioo`8001Yoo`00kGoo00<007ooOol057oo 0P006Woo003]Ool2000EOol00`00Oomoo`0IOol00>eoo`8001Aoo`8001]oo`00kWoo00<007ooOol0 4Goo0P0077oo003^Ool2000AOol3000LOol00>moo`<000ioo`@001aoo`00kWoo1@0037oo1P006goo 003]Ool3000017oo000000002Goo10000Woo0`006Woo003/Ool30003Ool>0004Ool3000IOol00>]o o`<000Eoo`/000Moo`<001Qoo`00jWoo0`002goo00<007ooOol02goo0`005goo003XOol4000KOol3 000FOol00>Moo`@001eoo`<001Eoo`00iWoo0`0087oo0`0057oo003UOol3000ROol3000COol00>Ao o`<002Aoo`<0019oo`00hgoo0`009Woo0`004Goo003ROol3000XOol3000@Ool00>5oo`<002Yoo`<0 00moo`00h7oo0`00;7oo0`003Woo003OOol3000^Ool3000=Ool00=ioo`<0031oo`<000aoo`00gGoo 0`007oo0`00 27oo003IOol3000jOol30007Ool00=Qood8000Ioo`00egooA0001Goo003oOolQOol00?moob5oo`00 ogoo8Goo003oOolQOol00?moob5oo`00f7oo@@001goo003HOom10007Ool00?moob5oo`00ogoo8Goo 003oOolQOol00?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {293.5, 0}} -> {-0.799828, -0.800269, \ 0.00321198, 0.00321198}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Elenco dei vincoli per ciascuna trave (sinistra, destra)", "Subsection"], Cell["\<\ Gli spostamenti al bordo ub sono descritti nella base {e1, e2}, non nelle \ basi adattate ai vincoli, utilizzando le componenti nelle basi adattate ai \ vincoli {d,n} (vedi la definizione di ub, sopra).\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[\(\((Append[\(ub[i]\)[#], \(\[Theta]b[i]\)[#]] /. vsp)\) &\)\ \ /@ \ {meno, pi\[UGrave]}, {i, 1, travi}], TableSpacing -> {4, 2, 2}]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(-\(ub\_d[1]\)["-"]\)}, {"0"}, {\(\(\[Theta]b[1]\)["-"]\)} }, RowSpacings->2, ColumnSpacings->1, RowAlignments->Baseline, ColumnAlignments->{Left}], GridBox[{ {"0"}, {"0"}, {"0"} }, RowSpacings->2, ColumnSpacings->1, RowAlignments->Baseline, ColumnAlignments->{Left}]} }, RowSpacings->4, ColumnSpacings->2, RowAlignments->Baseline, ColumnAlignments->{Left}], TableForm[ {{{ Times[ -1, Subscript[ ub, d][ 1][ "-"]], 0, \[Theta]b[ 1][ "-"]}, {0, 0, 0}}}, TableSpacing -> {4, 2, 2}]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(vincoli // Simplify\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(\(ub\_d[1]\)["+"] + \(ub\_n[1]\)["+"]\)\/\@2 == 0\)}, {\(\(\(ub\_d[1]\)["+"] - \(ub\_n[1]\)["+"]\)\/\@2 == 0\)}, {\(\(\[Theta]b[1]\)["+"] == 0\)}, {\(\(ub\_n[1]\)["-"] == 0\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ Times[ Power[ 2, Rational[ -1, 2]], Plus[ Subscript[ ub, d][ 1][ "+"], Subscript[ ub, n][ 1][ "+"]]], 0], Equal[ Times[ Power[ 2, Rational[ -1, 2]], Plus[ Subscript[ ub, d][ 1][ "+"], Times[ -1, Subscript[ ub, n][ 1][ "+"]]]], 0], Equal[ \[Theta]b[ 1][ "+"], 0], Equal[ Subscript[ ub, n][ 1][ "-"], 0]}], Editable->False]], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Generazione delle equazioni di bilancio al bordo", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Potenza residua al bordo", "Subsection", Evaluatable->False], Cell["\<\ Le forze al bordo sono da definire dopo la separazione tra forze attive e \ forze reattive\ \>", "SmallText"], Cell["\<\ Espressione della potenza totale residua per la soluzione bulk (soluzione \ generale delle equazioni differenziali di bilancio)\ \>", "SmallText"], Cell[BoxData[ \(pote := \[Sum]\+\(i = 1\)\%travi\((\((\(sb[i]\)[ pi\[UGrave]] . \(wb[i]\)[pi\[UGrave]])\) + \((\(sb[i]\)[ meno] . \(wb[i]\)[meno])\) + \(mb[i]\)[ pi\[UGrave]]\ \(\[Omega]b[i]\)[pi\[UGrave]] + \(mb[i]\)[ meno]\ \(\[Omega]b[i]\)[meno])\) // Simplify\)], "Input"], Cell[BoxData[ \(potbd := pote - \[Sum]\+\(i = 1\)\%travi\((\((\(s[i]\)[L[i]] . \(wb[i]\)[ pi\[UGrave]])\) - \((\(s[i]\)[0] . \(wb[i]\)[ meno])\) + \(m[i]\)[L[i]]\ \(\[Omega]b[i]\)[ pi\[UGrave]] - \(m[i]\)[0]\ \(\[Omega]b[i]\)[meno])\) // Simplify\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(pote\)], "Input"], Cell[BoxData[ \(\(mb[1]\)["-"]\ \(\[Omega]b[1]\)["-"] + \(mb[1]\)[ "+"]\ \(\[Omega]b[1]\)["+"] + \(sb\_d[1]\)["-"]\ \(wb\_d[1]\)[ "-"] + \(sb\_d[1]\)["+"]\ \(wb\_d[1]\)["+"] + \(sb\_n[1]\)[ "-"]\ \(wb\_n[1]\)["-"] + \(sb\_n[1]\)["+"]\ \(wb\_n[1]\)[ "+"]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Factor, Collect[potbd, ambd], {2}]\)], "Input"], Cell[BoxData[ \(\((\(mb[1]\)["-"] + \(sM[1]\)[0])\)\ \(\[Omega]b[1]\)[ "-"] + \((\(mb[1]\)[ "+"] - \(sM[1]\)[\[ScriptCapitalL]])\)\ \(\[Omega]b[1]\)["+"] + 1\/2\ \((\@2\ \(sN[1]\)[0] - \@2\ \(sQ[1]\)[0] + 2\ \(sb\_d[1]\)["-"])\)\ \(wb\_d[1]\)["-"] + 1\/2\ \((\@2\ \(sN[1]\)[\[ScriptCapitalL]] - \@2\ \(sQ[ 1]\)[\[ScriptCapitalL]] + 2\ \(sb\_d[1]\)["+"])\)\ \(wb\_d[ 1]\)["+"] + 1\/2\ \((\@2\ \(sN[1]\)[0] + \@2\ \(sQ[1]\)[0] + 2\ \(sb\_n[1]\)["-"])\)\ \(wb\_n[1]\)["-"] + 1\/2\ \((\@2\ \(sN[1]\)[\[ScriptCapitalL]] + \@2\ \(sQ[ 1]\)[\[ScriptCapitalL]] + 2\ \(sb\_n[1]\)["+"])\)\ \(wb\_n[ 1]\)["+"]\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Vincoli sugli atti di moto al bordo", "Subsection"], Cell["\<\ Si generano le equazioni di vincolo omogenee per gli atti di moto\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[\((# == 0)\) &, \(LinearEquationsToMatrices[vincoli, spbd]\)\[LeftDoubleBracket]1\[RightDoubleBracket] . spbd]\)], "Input"], Cell[BoxData[ \({\(ub\_d[1]\)["+"]\/\@2 + \(ub\_n[1]\)["+"]\/\@2 == 0, \(ub\_d[1]\)["+"]\/\@2 - \(ub\_n[1]\)["+"]\/\@2 == 0, \(\[Theta]b[1]\)["+"] == 0, \(ub\_n[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{ub = wb, \[Theta]b = \[Omega]b}, vincoli] // Simplify\)], "Input"], Cell[BoxData[ \({\(\(wb\_d[1]\)["+"] + \(wb\_n[1]\)["+"]\)\/\@2 == 0, \(\(wb\_d[1]\)["+"] - \(wb\_n[1]\)["+"]\)\/\@2 == 0, \(\[Omega]b[1]\)["+"] == 0, \(wb\_n[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell["Condizioni di vincolo sugli atti di moto", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(vam = \(Solve[\ Map[\((# == 0)\) &, \(LinearEquationsToMatrices[ Block[{ub = wb, \[Theta]b = \[Omega]b}, vincoli], ambd]\)\[LeftDoubleBracket]1\[RightDoubleBracket] . ambd], ambd]\)\[LeftDoubleBracket]1\[RightDoubleBracket] // Sort\)], "Input"], Cell[BoxData[ \({\(\[Omega]b[1]\)["+"] \[Rule] 0, \(wb\_d[1]\)["+"] \[Rule] 0, \(wb\_n[1]\)["-"] \[Rule] 0, \(wb\_n[1]\)["+"] \[Rule] 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ambdv = Complement[ambd /. vam, {0}]\)], "Input"], Cell[BoxData[ \({\(\[Omega]b[1]\)["-"], \(wb\_d[1]\)["-"]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Potenza al bordo per atti di moto vincolati", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(potbdv = Collect[potbd /. vam, ambdv]\)], "Input"], Cell[BoxData[ \(\((\(mb[1]\)["-"] + \(sM[1]\)[0])\)\ \(\[Omega]b[1]\)[ "-"] + \((\(sN[1]\)[0]\/\@2 - \(sQ[1]\)[0]\/\@2 + \(sb\_d[1]\)[ "-"])\)\ \(wb\_d[1]\)["-"]\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Equazioni di bilancio al bordo (corrispondenti agli atti di moto vincolati)\ \>", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(eqbilbd = \((#1 == 0 &)\) /@ Table[Coefficient[potbdv, ambdv\[LeftDoubleBracket]j\[RightDoubleBracket]], {j, 1, Length[ambdv]}]\)], "Input"], Cell[BoxData[ \({\(mb[1]\)["-"] + \(sM[1]\)[0] == 0, \(sN[1]\)[0]\/\@2 - \(sQ[1]\)[0]\/\@2 + \(sb\_d[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(eqbilbd /. bulksol // Simplify\)], "Input"], Cell[BoxData[ \({sMo[1] + \(mb[1]\)["-"] == 0, \(sNo[1] - sQo[1]\)\/\@2 + \(sb\_d[1]\)["-"] == 0}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Matrice delle equazioni di bilancio al bordo", "Subsection", Evaluatable->False], Cell["\<\ Vengono elencate le costanti di integrazione presenti nelle espressioni \ calcolate (per sicurezza vengono utilizzate le espressioni con le costanti C)\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(cNQM\)], "Input"], Cell[BoxData[ \({sNo[1], sQo[1], sMo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cNQMb = Complement[ Map[If[FreeQ[eqbilbd /. bulksol, #], 0, #]\ &, cNQM], {0}]\)], "Input"], Cell[BoxData[ \({sMo[1], sNo[1], sQo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(matbilbd = LinearEquationsToMatrices[eqbilbd /. bulksol, cNQMb]\)], "Input"], Cell[BoxData[ \({{{1, 0, 0}, {0, 1\/\@2, \(-\(1\/\@2\)\)}}, {\(-\(mb[1]\)["-"]\), \(-\(sb\_d[1]\)[ "-"]\)}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(If[Length[cNQMb] > 0, MatrixForm[ matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket]]]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "0", "0"}, {"0", \(1\/\@2\), \(-\(1\/\@2\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(If[Length[cNQMb] > 0, ColumnForm[ matbilbd\[LeftDoubleBracket]2\[RightDoubleBracket]]]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(-\(mb[1]\)["-"]\)}, {\(-\(sb\_d[1]\)["-"]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Times[ -1, mb[ 1][ "-"]], Times[ -1, Subscript[ sb, d][ 1][ "-"]]}], Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Rango della matrice delle equazioni di bilancio al bordo", "Subsection"], Cell["ordine del sistema delle equazioni differenziali di bilancio", \ "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(no = 3*travi\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell["\<\ numero di costanti nelle equazioni di bilancio al bordo per atti di moto \ vincolati (parametri dei descrittori della tensione da determinare) tale numero potrebbe risultare inferiore a no\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(nc = Length[cNQMb]\)], "Input"], Cell[BoxData[ \(3\)], "Output"] }, Open ]], Cell["\<\ numero di condizioni scalari di vincolo (o numero descrittori delle forze al \ bordo reattive)\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(nv = Length[vincoli]\)], "Input"], Cell[BoxData[ \(4\)], "Output"] }, Open ]], Cell["\<\ numero di descrittori degli atti di moto vincolati (o numero descrittori \ delle forze al bordo attive)\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(nf = Length[ambdv]\)], "Input"], Cell[BoxData[ \(2\)], "Output"] }, Open ]], Cell["controlli", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \({nf == Length[matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket]], nc == no, nf == 2 no - nv}\)], "Input"], Cell[BoxData[ \({True, True, True}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(rango = nc - Length[ If[Length[matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket]] > 0, NullSpace[matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket]], 0]]\)], "Input"], Cell[BoxData[ \(2\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Propriet\[AGrave] dei vincoli e delle forze attive", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(StylePrint[\n\t\ \ \ \ \ "\< no \[Rule] \>"\ <> \ ToString[no]\ <> \ \n\t"\<\n nc \[Rule] \>"\ <> \ ToString[nc]\ <> \ \n\t"\<\n nv \[Rule] \>"\ <> \ ToString[nv]\ <> \n\t"\<\n nf \[Rule] \>"\ <> \ ToString[nf]\ <> \n\t"\<\n rango \[Rule] \>" <> ToString[rango], \n\t FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]\)], "Input", CellOpen->False], Cell[BoxData[ \(" no \[Rule] 3\n nc \[Rule] 3\n nv \[Rule] 4\n nf \[Rule] 2\n rango \ \[Rule] 2"\)], "Output", CellFrame->True, FontSlant->"Plain", Background->RGBColor[0.979995, 1, 0]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(If[\((nf \[NotEqual] \((2 no - nv)\))\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\(\n\) \)\), "\n", \(\(If[\((nv < no)\) && \((rango == no)\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\), "\n", \(\(If[\((nv < no)\) && \((rango < no)\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\), "\n", \(\(If[\((nv == no)\) && \((rango == nf)\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\), "\n", \(\(If[\((nv == no)\) && \((rango < nf)\), StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\), "\n", \(\(If[\((nv > no)\) && \((rango == nf)\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\), "\n", \(\(If[\((nv > no)\) && \((rango < nf)\), \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\)}], "Input", CellOpen->False], Cell[BoxData[ \("Vincoli eccedenti (le forze attive al bordo possono essere qualsiasi)"\ \)], "Output", CellFrame->True, FontSlant->"Italic", Background->RGBColor[0.979995, 1, 0]] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forze assegnate al bordo [", StyleBox["D4", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Elenco delle forze attive al bordo", "Subsection"], Cell["Potenza delle forze al bordo in atti di moto vincolati", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Together, Collect[pote /. vam, ambdv], {2}] // Simplify\)], "Input"], Cell[BoxData[ \(\(mb[1]\)["-"]\ \(\[Omega]b[1]\)["-"] + \(sb\_d[1]\)["-"]\ \(wb\_d[1]\)[ "-"]\)], "Output"] }, Open ]], Cell["\<\ Forze attive al bordo (dalla espressione della potenza esterna si estraggono \ le forze corrispondenti a ciascun descrittore dell'atto di moto vincolato)\ \>", "SmallText"], Cell[BoxData[ \(\(fabd = Factor[Table[ Coefficient[pote /. vam, ambdv\[LeftDoubleBracket]j\[RightDoubleBracket]], {j, 1, Length[ambdv]}]];\)\)], "Input", CellFrame->False, Background->None], Cell[CellGroupData[{ Cell[BoxData[ \(If[Length[fabd] > 0, ColumnForm[fabd]]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(mb[1]\)["-"]\)}, {\(\(sb\_d[1]\)["-"]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { mb[ 1][ "-"], Subscript[ sb, d][ 1][ "-"]}], Editable->False]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Dati sulle forze assegnate al bordo [", StyleBox["D4", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell["\<\ Condizioni assegnate alle forze al bordo. Si tratta in genere della selezione \ di un sottoinsieme descritto da alcuni parametri, come f ad esempio, il cui \ valore verr\[AGrave] assegnato tra i dati numerici [ l'uso caratteri script \ per i parametri rende tutto molto pi\[UGrave] leggibile]. I DATI VANNO \ ASSEGNATI IN FORMA DI EQUAZIONI (per via delle condizioni di continuit\ \[AGrave])\ \>", "SmallText"], Cell[BoxData[ \(\(forze = {\ };\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[TextData[{ "Una assegnazione esplicita dei dati sulle forze \[EGrave] la lista \ seguente, data qui come esempio e non assegnata a ", StyleBox["forze", FontFamily->"Courier New"], ". Con ", StyleBox["sb", FontFamily->"Courier New"], " si intende il vettore forza al bordo." }], "SmallText"], Cell[BoxData[ \(\({\((\(sb[1]\)[pi\[UGrave]] + \(sb[2]\)[meno])\) . e\_1 == 0, \((\(sb[1]\)[pi\[UGrave]] + \(sb[2]\)[meno])\) . e\_2 == 0, \(mb[1]\)[meno] == 0, \(mb[1]\)[pi\[UGrave]] == 0, \(mb[2]\)[meno] == 0, \(mb[2]\)[pi\[UGrave]] == 0, \(sb[2]\)[pi\[UGrave]] . \(d[2]\)[pi\[UGrave]] == 0};\)\)], "Input", CellFrame->True, Background->None], Cell["\<\ I dati sulle forze sono tradotti in una lista di sostituzioni\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(fabdp1 = \(Solve[forze, fbd]\)\[LeftDoubleBracket]1\[RightDoubleBracket] // Sort\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell["\<\ Si controlla che tutti i valori siano stati assegnati e si assegna il valore \ nullo ai rimanenti\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(Select[ fabd /. fabdp1, \((Length[Intersection[Variables[# /. fabdp1], fbd]] > 0)\)\ &]\)], "Input"], Cell[BoxData[ \({\(mb[1]\)["-"], \(sb\_d[1]\)["-"]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(fabdp = Join[fabdp1, \(Solve[Map[\((# \[Equal] 0)\)\ &, %], fbd]\)\[LeftDoubleBracket]1\[RightDoubleBracket]] // Sort\)], "Input"], Cell[BoxData[ \({\(mb[1]\)["-"] \[Rule] 0, \(sb\_d[1]\)["-"] \[Rule] 0}\)], "Output"] }, Open ]], Cell["Si fa un controllo finale", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(fabd /. fabdp\)], "Input"], Cell[BoxData[ \({0, 0}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Test di compatibilit\[AGrave] dei dati sulle forze", "Subsection"], Cell["\<\ Il termine noto deve appartenere all'immagine, ovvero deve essere ortogonale \ allo spazio nullo della trasposta\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(ker = Block[{ker0 = If[nc > 0, NullSpace[ Transpose[ matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket]]], {}]}, If[Length[ker0] > 0, ker0, {Array[0\ &, nf]}]]\)], "Input"], Cell[BoxData[ \({{0, 0}}\)], "Output"] }, Open ]], Cell["\<\ prodotto scalare dei vettori base del nucleo della trasposta per il termine \ noto; ciascun prodotto deve essere nullo; si selezionano i prodotti non nulli\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(spro = Complement[ ker . matbilbd\[LeftDoubleBracket]2\[RightDoubleBracket] /. fabdp // Flatten, {0}]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell[BoxData[ \(If[\((nf > rango)\), If[\((Length[spro] > 0)\), \n\t StylePrint["\", FontWeight \[Rule] "\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[1]]; Interrupt[], \n\t StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]]]\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Soluzione delle equazioni di bilancio al bordo ", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Equazioni di bilancio al bordo", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(eqbilbd /. bulksol\) /. fabdp // Simplify\)], "Input"], Cell[BoxData[ \({sMo[1] == 0, \(sNo[1] - sQo[1]\)\/\@2 == 0}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Soluzione delle equazioni di bilancio al bordo ", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(If[\((nf == nc)\) && \((rango == nf)\) && \((nc > 0)\), cNQMsol = LinearSolve[matbilbd\[LeftDoubleBracket]1\[RightDoubleBracket], matbilbd\[LeftDoubleBracket]2\[RightDoubleBracket] /. fabdp]; \n\t cNQMval = Table[cNQMb\[LeftDoubleBracket]i\[RightDoubleBracket] \[Rule] cNQMsol\[LeftDoubleBracket]i\[RightDoubleBracket], {i, 1, Length[cNQMb]}], \n\t cNQMval = \(Solve[\(eqbilbd /. bulksol\) /. fabdp, cNQMb]\)\[LeftDoubleBracket]1\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ \({sNo[1] \[Rule] sQo[1], sMo[1] \[Rule] 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{\(sN[i]\)[\[Zeta]], \(sQ[i]\)[\[Zeta]], \(sM[i]\)[\[Zeta]]} /. bulksol, {i, 1, travi}] // Simplify\)], "Input"], Cell[BoxData[ \({{\(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + sNo[1], \(-\(\(\[ScriptB]\ \[Zeta]\)\/\@2\)\) + sQo[1], \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) + sMo[1] - \[Zeta]\ sQo[1]}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cNQMval\)], "Input"], Cell[BoxData[ \({sNo[1] \[Rule] sQo[1], sMo[1] \[Rule] 0}\)], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Funzioni di risposta e soluzione generale per lo spostamento (bulk)\ \>", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Spostamento e gradiente", "Subsection"], Cell[BoxData[ \(\(u[ i_]\)[\[Zeta]_] := \(u\_1[i]\)[\[Zeta]]\ a\_1[ i] + \(u\_2[i]\)[\[Zeta]]\ a\_2[i]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"grad", "=", RowBox[{"{", RowBox[{ RowBox[{\(\[Epsilon][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(u\_1[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}], ",", RowBox[{\(\[Gamma][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ RowBox[{ SuperscriptBox[\(u\_2[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "-", \(\(\[Theta][i]\)[\[Zeta]]\)}]}], "]"}]}], ",", RowBox[{\(\[Chi][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(\[Theta][i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{\(\[Epsilon][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(u\_1[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}], ",", RowBox[{\(\[Gamma][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ RowBox[{ SuperscriptBox[\(u\_2[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "-", \(\(\[Theta][i]\)[\[Zeta]]\)}]}], "]"}]}], ",", RowBox[{\(\[Chi][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(\[Theta][i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Funzioni di risposta e vincolo di Bernoulli", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(risp = {sNf[i_] \[Rule] Function[\[Zeta], YA[i]\ \(\[Epsilon][i]\)[\[Zeta]]], \n\t\tsMf[ i_] \[Rule] Function[\[Zeta], YJ[i]\ \(\[Chi][i]\)[\[Zeta]]]}\)], "Input"], Cell[BoxData[ \({sNf[i_] \[Rule] Function[\[Zeta], YA[i]\ \(\[Epsilon][i]\)[\[Zeta]]], sMf[i_] \[Rule] Function[\[Zeta], YJ[i]\ \(\[Chi][i]\)[\[Zeta]]]}\)], "Output"] }, Open ]], Cell["Vincolo di scorrimento nullo (Modello di Eulero-Bernoulli)", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"vinBer", "=", RowBox[{"{", RowBox[{\(\[Theta][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(u\_2[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\[Theta][i_]\), "\[Rule]", RowBox[{"Function", "[", RowBox[{"\[Zeta]", ",", RowBox[{ SuperscriptBox[\(u\_2[i]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], "]"}]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Soluzione generale", "Subsection"], Cell["\<\ Prima della sostisuzione delle soluzioni delle equazioni di bilancio al bordo \ e del vincolo di Eulero-Bernoulli\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Table[{\(sN[i]\)[\[Zeta]] == \(sNf[i]\)[\[Zeta]], \(sM[ i]\)[\[Zeta]] == \(sMf[i]\)[\[Zeta]]}, {i, 1, travi}] /. bulksol\) /. risp // Flatten\) // Simplify\)], "Input"], Cell[BoxData[ \({sNo[ 1] == \(\[ScriptB]\ \[Zeta]\)\/\@2 + \(\[ScriptCapitalY]\ \[ScriptCapitalJ]\ \(\[Epsilon][1]\)[\[Zeta]]\)\/\(\[ScriptCapitalL]\^2\ \ \[Kappa]\), \(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) + sMo[1] == \[Zeta]\ sQo[ 1] + \[ScriptCapitalY]\[ScriptCapitalJ]\ \(\[Chi][ 1]\)[\[Zeta]]}\)], "Output"] }, Open ]], Cell["\<\ Prima della sostituzione delle soluzioni delle equazioni di bilancio al bordo\ \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqnspO = \(\(\(\(Table[{\(sN[i]\)[\[Zeta]] == \(sNf[i]\)[\[Zeta]], \(sM[ i]\)[\[Zeta]] == \(sMf[i]\)[\[Zeta]]}, {i, 1, travi}] /. bulksol\) /. risp\) /. grad\) /. vinBer // Flatten\) // Simplify\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{\(sNo[1]\), "==", RowBox[{\(\(\[ScriptB]\ \[Zeta]\)\/\@2\), "+", FractionBox[ RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_1[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], \(\[ScriptCapitalL]\^2\ \[Kappa]\)]}]}], ",", RowBox[{\(\(\[ScriptB]\ \[Zeta]\^2\)\/\(2\ \@2\) + sMo[1]\), "==", RowBox[{\(\[Zeta]\ sQo[1]\), "+", RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_2[1]\), "\[Prime]\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}]}]}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(spsolDO = \(DSolve[eqnspO, Flatten[Table[{u\_1[i], u\_2[i]}, {i, 1, travi}]], \[Zeta], DSolveConstants \[Rule] \[ScriptCapitalD]]\)\[LeftDoubleBracket]1\ \[RightDoubleBracket] // Simplify\)], "Input"], Cell[BoxData[ \({u\_1[1] \[Rule] Function[{\[Zeta]}, \(\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \ \[Zeta]\^2\ \[Kappa]\)\/\@2\)\) + 2\ \[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \ sNo[1]\)\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + \[ScriptCapitalD][1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\(-\(\(\[ScriptB]\ \[Zeta]\^4\)\/\(6\ \ \@2\)\)\) - 2\ \[Zeta]\^2\ sMo[1] + 2\/3\ \[Zeta]\^3\ sQo[ 1]\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\) + \ \[ScriptCapitalD][2] + \[Zeta]\ \[ScriptCapitalD][3]]}\)], "Output"] }, Open ]], Cell["\<\ Dopo la sostisuzione delle soluzioni delle equazioni di bilancio al bordo\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqnsp = \(\(\(\(\(Table[{\(sN[i]\)[\[Zeta]] == \(sNf[ i]\)[\[Zeta]], \(sM[i]\)[\[Zeta]] == \(sMf[ i]\)[\[Zeta]]}, {i, 1, travi}] /. bulksol\) /. cNQMval\) /. risp\) /. grad\) /. vinBer // Flatten\) // Simplify\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{\(sQo[1]\), "==", RowBox[{\(\(\[ScriptB]\ \[Zeta]\)\/\@2\), "+", FractionBox[ RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_1[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], \(\[ScriptCapitalL]\^2\ \[Kappa]\)]}]}], ",", RowBox[{\(1\/4\ \[Zeta]\ \((\@2\ \[ScriptB]\ \[Zeta] - 4\ sQo[1])\)\), "==", RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_2[1]\), "\[Prime]\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}]}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(spsolD = \(DSolve[eqnsp, Flatten[Table[{u\_1[i], u\_2[i]}, {i, 1, travi}]], \[Zeta], DSolveConstants \[Rule] \[ScriptCapitalD]]\)\[LeftDoubleBracket]1\ \[RightDoubleBracket] // Simplify\)], "Input"], Cell[BoxData[ \({u\_1[1] \[Rule] Function[{\[Zeta]}, \(\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \ \[Zeta]\^2\ \[Kappa]\)\/\@2\)\) + 2\ \[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \ sQo[1]\)\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + \[ScriptCapitalD][1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\(-\(\(\[ScriptB]\ \[Zeta]\^4\)\/\(6\ \ \@2\)\)\) + 2\/3\ \[Zeta]\^3\ sQo[ 1]\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\) + \ \[ScriptCapitalD][2] + \[Zeta]\ \[ScriptCapitalD][3]]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(splist = Table[{\(u\_1[i]\)[\[Zeta]], \(u\_2[i]\)[\[Zeta]], \(\[Theta][ i]\)[\[Zeta]]}, {i, 1, travi}] // Flatten\)], "Input"], Cell[BoxData[ \({\(u\_1[1]\)[\[Zeta]], \(u\_2[1]\)[\[Zeta]], \(\[Theta][ 1]\)[\[Zeta]]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(splist /. vinBer\) /. spsolDO // Simplify\)], "Input"], Cell[BoxData[ \({\(-\(\(\[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \((\@2\ \[ScriptB]\ \ \[Zeta] - 4\ sNo[1])\)\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\ \)\) + \[ScriptCapitalD][ 1], \(\@2\ \[ScriptB]\ \[Zeta]\^4 + 24\ \[Zeta]\^2\ sMo[1] - 8\ \ \[Zeta]\^3\ sQo[1] + 48\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \[ScriptCapitalD][2] + 48\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Zeta]\ \ \[ScriptCapitalD][3]\)\/\(48\ \[ScriptCapitalY]\[ScriptCapitalJ]\), \(\@2\ \ \[ScriptB]\ \[Zeta]\^3 + 12\ \[Zeta]\ sMo[1] - 6\ \[Zeta]\^2\ sQo[1] + 12\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[ScriptCapitalD][3]\)\/\(12\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(splist /. vinBer\) /. spsolD // Simplify\)], "Input"], Cell[BoxData[ \({\(-\(\(\[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \((\@2\ \[ScriptB]\ \ \[Zeta] - 4\ sQo[1])\)\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\ \)\) + \[ScriptCapitalD][ 1], \(\[ScriptB]\ \[Zeta]\^4\)\/\(24\ \@2\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) - \(\[Zeta]\^3\ sQo[1]\)\/\(6\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) + \[ScriptCapitalD][ 2] + \[Zeta]\ \[ScriptCapitalD][ 3], \(\@2\ \[ScriptB]\ \[Zeta]\^3 - 6\ \[Zeta]\^2\ sQo[1] + 12\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[ScriptCapitalD][3]\)\/\(12\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Cambiamento delle costanti di integrazione", "Subsection"], Cell["\<\ Viene costruita la lista delle costanti di integrazione delle funzioni di \ risposta. La lista delle costanti di integrazione presenti nelle condizioni di vincolo \ in generale contiene la prima.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(cDlistO = Complement[ Map[If[FreeQ[\(splist /. vinBer\) /. spsolD, #], 0, #]\ &, Table[\[ScriptCapitalD][i], {i, 3\ travi}]], {0}]\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalD][1], \[ScriptCapitalD][2], \[ScriptCapitalD][ 3]}\)], "Output"] }, Open ]], Cell["\<\ Vengono elencate le costanti di integrazione presenti nelle espressioni \ calcolate\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(cDlist = Block[{splistV = \(splist /. vinBer\) /. spsolD}, Join[\n\tComplement[ Map[If[FreeQ[splistV, #], 0, #]\ &, cNQM], {0}], \n\t Complement[ Map[If[FreeQ[splistV, #], 0, #]\ &, cDlistO], {0}]\n]] // Union\)], "Input"], Cell[BoxData[ \({sQo[1], \[ScriptCapitalD][1], \[ScriptCapitalD][2], \[ScriptCapitalD][ 3]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Table[\({\(u\_1[i]\)[0] \[Equal] uo\_1[i], \(u\_2[i]\)[0] \[Equal] uo\_2[i], \(\[Theta][i]\)[0] \[Equal] \[Theta]o[i]} /. vinBer\) /. spsolD, {i, 1, travi}] // Simplify\) // Flatten\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalD][1] == uo\_1[1], \[ScriptCapitalD][2] == uo\_2[1], \[ScriptCapitalD][3] == \[Theta]o[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(fromDtoU = \(Solve[%, cDlistO]\)\_\(\(\[LeftDoubleBracket]\)\(1\)\(\ \[RightDoubleBracket]\)\)\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalD][1] \[Rule] uo\_1[1], \[ScriptCapitalD][2] \[Rule] uo\_2[1], \[ScriptCapitalD][3] \[Rule] \[Theta]o[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cRlist = cDlist /. fromDtoU\)], "Input"], Cell[BoxData[ \({sQo[1], uo\_1[1], uo\_2[1], \[Theta]o[1]}\)], "Output"] }, Open ]], Cell["\<\ Prima della sostituzione delle soluzioni delle equazioni di bilancio al bordo\ \ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(spsolO = spsolDO /. fromDtoU\)], "Input"], Cell[BoxData[ \({u\_1[1] \[Rule] Function[{\[Zeta]}, \(\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \ \[Zeta]\^2\ \[Kappa]\)\/\@2\)\) + 2\ \[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \ sNo[1]\)\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + uo\_1[1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\(-\(\(\[ScriptB]\ \[Zeta]\^4\)\/\(6\ \ \@2\)\)\) - 2\ \[Zeta]\^2\ sMo[1] + 2\/3\ \[Zeta]\^3\ sQo[ 1]\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\) + uo\_2[1] + \[Zeta]\ \[Theta]o[1]]}\)], "Output"] }, Open ]], Cell["\<\ Dopo la sostisuzione delle soluzioni delle equazioni di bilancio al bordo\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(spsol = spsolD /. fromDtoU\)], "Input"], Cell[BoxData[ \({u\_1[1] \[Rule] Function[{\[Zeta]}, \(\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \ \[Zeta]\^2\ \[Kappa]\)\/\@2\)\) + 2\ \[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ \ sQo[1]\)\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + uo\_1[1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(\(-\(\(\[ScriptB]\ \[Zeta]\^4\)\/\(6\ \ \@2\)\)\) + 2\/3\ \[Zeta]\^3\ sQo[ 1]\)\/\(4\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\) + uo\_2[1] + \[Zeta]\ \[Theta]o[1]]}\)], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Soluzione delle equazioni di vincolo ", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Equazioni di vincolo", "Subsection", Evaluatable->False], Cell["\<\ Le variabili che hanno il significato di spostamenti al bordo vengono \ sostituite con i valori al bordo dello spostamento\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqvinO = Block[{\n\t\tub = \((Function[ j, \((Switch[j, meno, \(u[#]\)[0], pi\[UGrave], \(u[#]\)[ L[#]]])\)] &)\), \[Theta]b = \((Function[ j, \((Switch[j, meno, \(\[Theta][#]\)[0], pi\[UGrave], \(\[Theta][#]\)[L[#]]])\)] &)\)\n\t\t}, vincoli] // Simplify\)], "Input"], Cell[BoxData[ \({\(u\_1[1]\)[\[ScriptCapitalL]] == 0, \(u\_2[1]\)[\[ScriptCapitalL]] == 0, \(\[Theta][1]\)[\[ScriptCapitalL]] == 0, \(\(u\_1[1]\)[0] + \(u\_2[1]\)[0]\)\/\@2 == 0}\)], "Output"] }, Open ]], Cell["\<\ Qui \[EGrave] essenziale che \"vincoli\" sia stata definita con \":=\" e \ utilizzando il prodotto scalare invece che i nomi delle componenti dello \ spostamento.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(eqvin = \(eqvinO /. vinBer\) /. spsol // Simplify\)], "Input"], Cell[BoxData[ \({uo\_1[ 1] == \(\[ScriptCapitalL]\^3\ \[Kappa]\ \((\@2\ \[ScriptB]\ \ \[ScriptCapitalL] - 4\ sQo[1])\)\)\/\(4\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\), \(\[ScriptB]\ \ \[ScriptCapitalL]\^4\)\/\(24\ \@2\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + \ \[ScriptCapitalL]\ \[Theta]o[1] + uo\_2[1] == \(\[ScriptCapitalL]\^3\ sQo[1]\)\/\(6\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\), \(\@2\ \[ScriptB]\ \[ScriptCapitalL]\^3 \ - 6\ \[ScriptCapitalL]\^2\ sQo[1] + 12\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \[Theta]o[1]\)\/\(12\ \[ScriptCapitalY]\[ScriptCapitalJ]\) == 0, \(uo\_1[1] + uo\_2[1]\)\/\@2 == 0}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Matrice delle equazioni di vincolo", "Subsection", Evaluatable->False], Cell[BoxData[ \(\(matvin = LinearEquationsToMatrices[eqvin, cRlist] // Simplify;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(MatrixForm[matvin\[LeftDoubleBracket]1\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[ScriptCapitalL]\^3\ \[Kappa]\)\/\[ScriptCapitalY]\ \[ScriptCapitalJ]\), "1", "0", "0"}, {\(-\(\[ScriptCapitalL]\^3\/\(6\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)\), "0", "1", "\[ScriptCapitalL]"}, {\(-\(\[ScriptCapitalL]\^2\/\(2\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)\), "0", "0", "1"}, {"0", \(1\/\@2\), \(1\/\@2\), "0"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ColumnForm[matvin\[LeftDoubleBracket]2\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(\[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(2\ \@2\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)}, {\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^4\)\/\(24\ \@2\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\)}, {\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^3\)\/\(6\ \@2\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\)}, {"0"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Times[ Rational[ 1, 2], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalL], 4], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], \[Kappa]], Times[ Rational[ -1, 24], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalL], 4], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1]], Times[ Rational[ -1, 6], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalL], 3], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1]], 0}], Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Length[ Transpose[matvin\[LeftDoubleBracket]1\[RightDoubleBracket]]]\)], "Input"], Cell[BoxData[ \(4\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cRnull = NullSpace[matvin\[LeftDoubleBracket]1\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cRlist\)], "Input"], Cell[BoxData[ \({sQo[1], uo\_1[1], uo\_2[1], \[Theta]o[1]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Propriet\[AGrave] della soluzione", "Subsection"], Cell[BoxData[ \(\(If[Length[cRnull] > 0, StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\)], "Input"], Cell[BoxData[ \(\(If[nv > Length[cRlist], StylePrint["\", FontSlant \[Rule] "\", CellFrame \[Rule] True, Background \[Rule] Hue[0.17]]];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Soluzione delle equazioni di vincolo", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(cRsol0 = LinearSolve[matvin\[LeftDoubleBracket]1\[RightDoubleBracket], matvin\[LeftDoubleBracket]2\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ \({\(3\ \((\[ScriptB]\ \[ScriptCapitalL] + 4\ \[ScriptB]\ \ \[ScriptCapitalL]\ \[Kappa])\)\)\/\(8\ \((\@2 + 3\ \@2\ \[Kappa])\)\), \(\ \[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \((\@2 + 3\ \@2\ \[Kappa])\)\), \(-\(\(\[ScriptB]\ \ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \((\@2 + 3\ \@2\ \[Kappa])\)\)\)\), \(\[ScriptB]\ \[ScriptCapitalL]\^3 + 12\ \ \[ScriptB]\ \[ScriptCapitalL]\^3\ \[Kappa]\)\/\(48\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \((\@2 + 3\ \@2\ \[Kappa])\)\)}\)], "Output"] }, Open ]], Cell[BoxData[ \(Clear[cA]\)], "Input"], Cell[BoxData[ \(\(cRsol1 = Array[cA[#] &, Length[cRnull]] . cRnull;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(cRsol = If[Length[cRnull] > 0, cRsol0 + cRsol1, cRsol0]\)], "Input"], Cell[BoxData[ \({\(3\ \((\[ScriptB]\ \[ScriptCapitalL] + 4\ \[ScriptB]\ \ \[ScriptCapitalL]\ \[Kappa])\)\)\/\(8\ \((\@2 + 3\ \@2\ \[Kappa])\)\), \(\ \[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \((\@2 + 3\ \@2\ \[Kappa])\)\), \(-\(\(\[ScriptB]\ \ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \((\@2 + 3\ \@2\ \[Kappa])\)\)\)\), \(\[ScriptB]\ \[ScriptCapitalL]\^3 + 12\ \ \[ScriptB]\ \[ScriptCapitalL]\^3\ \[Kappa]\)\/\(48\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \((\@2 + 3\ \@2\ \[Kappa])\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cRval = Table[cRlist\[LeftDoubleBracket]i\[RightDoubleBracket] \[Rule] cRsol\[LeftDoubleBracket]i\[RightDoubleBracket], {i, 1, Length[cRlist]}] // Simplify\)], "Input"], Cell[BoxData[ \({sQo[ 1] \[Rule] \(3\ \[ScriptB]\ \[ScriptCapitalL]\ \((1 + 4\ \ \[Kappa])\)\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\), uo\_1[1] \[Rule] \(\[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(\@2\ \ \((8\ \[ScriptCapitalY]\[ScriptCapitalJ] + 24\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \[Kappa])\)\), uo\_2[1] \[Rule] \(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^4\ \ \[Kappa]\)\/\(8\ \@2\ \((\[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Kappa])\)\)\)\), \ \[Theta]o[ 1] \[Rule] \(\[ScriptB]\ \[ScriptCapitalL]\^3\ \((1 + 12\ \[Kappa])\ \)\)\/\(48\ \@2\ \((\[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \[Kappa])\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(\(splist /. vinBer\) /. spsol\) /. cRval // Simplify\) // Factor\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \((\[ScriptCapitalL] - \ \[Zeta])\)\ \[Kappa]\ \((\[ScriptCapitalL] + 4\ \[Zeta] + 12\ \[Zeta]\ \[Kappa])\)\)\/\(8\ \@2\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\)\)}, {\(-\(\(\[ScriptB]\ \((\[ScriptCapitalL] - \[Zeta])\)\^2\ \((\(-\ \[ScriptCapitalL]\)\ \[Zeta] - 2\ \[Zeta]\^2 + 6\ \[ScriptCapitalL]\^2\ \[Kappa] - 6\ \[Zeta]\^2\ \[Kappa])\)\)\/\(48\ \@2\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\)\)\)}, {\(\(\[ScriptB]\ \((\(-\[ScriptCapitalL]\) + \[Zeta])\)\ \((\(-\ \[ScriptCapitalL]\^2\) - \[ScriptCapitalL]\ \[Zeta] + 8\ \[Zeta]\^2 - 12\ \[ScriptCapitalL]\^2\ \[Kappa] - 12\ \[ScriptCapitalL]\ \[Zeta]\ \[Kappa] + 24\ \[Zeta]\^2\ \[Kappa])\)\)\/\(48\ \@2\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\)\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Times[ Rational[ 1, 8], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalL], 2], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], Plus[ \[ScriptCapitalL], Times[ -1, \[Zeta]]], \[Kappa], Power[ Plus[ 1, Times[ 3, \[Kappa]]], -1], Plus[ \[ScriptCapitalL], Times[ 4, \[Zeta]], Times[ 12, \[Zeta], \[Kappa]]]], Times[ Rational[ -1, 48], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], Power[ Plus[ \[ScriptCapitalL], Times[ -1, \[Zeta]]], 2], Power[ Plus[ 1, Times[ 3, \[Kappa]]], -1], Plus[ Times[ -1, \[ScriptCapitalL], \[Zeta]], Times[ -2, Power[ \[Zeta], 2]], Times[ 6, Power[ \[ScriptCapitalL], 2], \[Kappa]], Times[ -6, Power[ \[Zeta], 2], \[Kappa]]]], Times[ Rational[ 1, 48], Power[ 2, Rational[ -1, 2]], \[ScriptB], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], Plus[ Times[ -1, \[ScriptCapitalL]], \[Zeta]], Power[ Plus[ 1, Times[ 3, \[Kappa]]], -1], Plus[ Times[ -1, Power[ \[ScriptCapitalL], 2]], Times[ -1, \[ScriptCapitalL], \[Zeta]], Times[ 8, Power[ \[Zeta], 2]], Times[ -12, Power[ \[ScriptCapitalL], 2], \[Kappa]], Times[ -12, \[ScriptCapitalL], \[Zeta], \[Kappa]], Times[ 24, Power[ \[Zeta], 2], \[Kappa]]]]}], Editable->False]], "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Espressioni delle soluzioni (N, Q, M), (u, v, \[Theta]), (forze al bordo) \ \>", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[TextData[{ "Definizione di extraSimplify [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell[BoxData[ \(\(extraSimplify = \((Simplify[ Cancel[TrigExpand[#]]]\ &)\);\)\)], "Input"], Cell[BoxData[ \(\(extraSimplify = \((Simplify[N[#]]\ &)\);\)\)], "Input"], Cell[BoxData[ \(\(extraSimplify = \((Expand[N[#]]\ &)\);\)\)], "Input"], Cell[BoxData[ \(\(extraSimplify = Apart;\)\)], "Input"], Cell[BoxData[ \(\(simplifyDirac[\[Zeta]_, Lo_, Li_]\)[expr1__] := Module[{g}, Simplify[\(Distribute[\[Integral]\_Lo\%Li\((Distribute[\ Factor[ expr1]\ g[\[Zeta]]])\) \[DifferentialD]\[Zeta]] /. \ \[Integral]\_Lo\%Li g[\[Zeta]] anyexpr_ \[DifferentialD]\[Zeta] \[Rule] anyexpr\) /. \[Integral]\_Lo\%Li g[\[Zeta]] \[DifferentialD]\[Zeta] \[Rule] 1]]\)], "Input"], Cell[BoxData[ \(\(extraSimplify = \((#\ &)\);\)\)], "Input"], Cell[BoxData[ \(\(extraSimplify = simplifyDirac[\[Zeta], 0, L[i]];\)\)], "Input"], Cell[BoxData[ \(\(extraSimplify = \((Simplify[ Collect[#, {DiracDelta[__], UnitStep[__]}]]\ &)\);\)\)], "Input"], Cell["\<\ Selezione automatica della funzione di semplificazione extraSimplify, basata \ sulla verifica della presenza di UnitStep o DiracDelta nella espressione di \ N, Q, M\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(If[FreeQ[\((#[\[Zeta]]\ &)\) /@ svar /. bulksolC, UnitStep] && FreeQ[\((#[\[Zeta]]\ &)\) /@ svar /. bulksolC, DiracDelta], extraSimplify = \((#\ &)\), extraSimplify = \((Simplify[ Collect[#, {DiracDelta[__], UnitStep[__]}]]\ &)\)]\)], "Input"], Cell[BoxData[ \(#1 &\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Espressioni delle costanti di integrazione", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Factor, \(cNQMval // Simplify\) // extraSimplify, {2}]\)], "Input"], Cell[BoxData[ \({sNo[1] \[Rule] sQo[1], sMo[1] \[Rule] 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Factor, \(cRval // Simplify\) // extraSimplify, {2}]\)], "Input"], Cell[BoxData[ \({sQo[ 1] \[Rule] \(3\ \[ScriptB]\ \[ScriptCapitalL]\ \((1 + 4\ \ \[Kappa])\)\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\), uo\_1[1] \[Rule] \(\[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \ \@2\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\), uo\_2[1] \[Rule] \(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^4\ \ \[Kappa]\)\/\(8\ \@2\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\)\)\), \[Theta]o[ 1] \[Rule] \(\[ScriptB]\ \[ScriptCapitalL]\^3\ \((1 + 12\ \[Kappa])\ \)\)\/\(48\ \@2\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((1 + 3\ \[Kappa])\)\)}\ \)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Sollecitazioni", "Subsection"], Cell[CellGroupData[{ Cell["Forza normale", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(sN[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments \[Rule] Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(\(\@2\ \[ScriptB]\ \((3\ \[ScriptCapitalL]\ \ \((1 + 4\ \[Kappa])\) - 8\ \((\[Zeta] + 3\ \[Zeta]\ \[Kappa])\))\)\)\/\(16 + 48\ \[Kappa]\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Forza di taglio", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(sQ[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(\(\@2\ \[ScriptB]\ \((3\ \[ScriptCapitalL]\ \ \((1 + 4\ \[Kappa])\) - 8\ \((\[Zeta] + 3\ \[Zeta]\ \[Kappa])\))\)\)\/\(16 + 48\ \[Kappa]\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Momento", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(sM[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(\(\@2\ \[ScriptB]\ \[Zeta]\ \((\(-3\)\ \ \[ScriptCapitalL]\ \((1 + 4\ \[Kappa])\) + 4\ \((\[Zeta] + 3\ \[Zeta]\ \[Kappa])\))\)\)\/\(16 + 48\ \[Kappa]\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Spostamenti", "Subsection"], Cell[CellGroupData[{ Cell["Spostamento assiale", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(u\_1[i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(\(\[ScriptB]\ \[ScriptCapitalL]\^2\ \((\ \[ScriptCapitalL] - \[Zeta])\)\ \[Kappa]\ \((\[ScriptCapitalL] + 4\ \((\[Zeta] + 3\ \[Zeta]\ \[Kappa])\))\)\)\/\(8\ \@2\ \((\ \[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Kappa])\)\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Spostamento trasversale", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(u\_2[i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(-\(\(\[ScriptB]\ \((\[ScriptCapitalL] - \ \[Zeta])\)\^2\ \((\(-\[ScriptCapitalL]\)\ \[Zeta] + 6\ \[ScriptCapitalL]\^2\ \[Kappa] - 2\ \[Zeta]\^2\ \((1 + 3\ \[Kappa])\))\)\)\/\(48\ \@2\ \((\ \[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \[Kappa])\)\)\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Rotazione", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[{"\" <> ToString[ i], \(\(\(\(\[Theta][i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify}, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \(\(\[ScriptB]\ \((8\ \[Zeta]\^3\ \((1 + 3\ \[Kappa])\) - 9\ \[ScriptCapitalL]\ \[Zeta]\^2\ \((1 + 4\ \[Kappa])\) + \[ScriptCapitalL]\^3\ \((1 + 12\ \[Kappa])\))\)\)\/\(48\ \@2\ \((\ \[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Kappa])\)\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Forze e momenti al bordo calcolati (parte attiva e parte reattiva)\ \>", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(Definition[extraSimplify]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(extraSimplify = #1 &\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ extraSimplify], Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Forze (bordo sinistro e bordo destro)", "Subsubsection"], Cell["Le componenti sono nella base {e1, e2}", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[\(\(\({"\" <> ToString[i], \(-\(s[i]\)[0]\), \(s[i]\)[ L[i]]} /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments \[Rule] Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \({0, \(3\ \[ScriptB]\ \[ScriptCapitalL]\ \((1 \ + 4\ \[Kappa])\)\)\/\(8 + 24\ \[Kappa]\)}\), \({0, \(\[ScriptB]\ \ \[ScriptCapitalL]\ \((5 + 12\ \[Kappa])\)\)\/\(8 + 24\ \[Kappa]\)}\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Momenti (bordo sinistro e bordo destro)", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[\(\(\({"\" <> ToString[i], \(-\(m[i]\)[0]\), \(m[i]\)[ L[i]]} /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments \[Rule] Left]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", "0", \(\(\[ScriptB]\ \[ScriptCapitalL]\^2\)\/\(\@2\ \((8 + 24\ \[Kappa])\)\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Verifiche: forza risultante", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[\(\(\({"\" <> ToString[i], \(-\(s[i]\)[0]\) + \(s[i]\)[ L[i]] + \[Integral]\_0\%\(L[i]\)Evaluate[\(b[ i]\)[\[Zeta]]] \[DifferentialD]\[Zeta]} /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify, \n\t{i, 1, travi}], TableDepth -> 2, TableAlignments -> Center]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", \({0, 0}\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Center}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Center]]]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Verifiche: momento risultante", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Table[extraSimplify[ Simplify[\(\({"\" <> ToString[i], \(-\(m[i]\)[0]\) + \(m[i]\)[ L[i]] + \(s[i]\)[L[i]] . a\_2[i]\ L[ i] + \[Integral]\_0\%\(L[i]\)\(\(b[i]\)[\[Zeta]] . a\_2[i]\ \[Zeta]\) \[DifferentialD]\[Zeta] + \ \[Integral]\_0\%\(L[i]\)\(c[ i]\)[\[Zeta]] \[DifferentialD]\[Zeta]} \ /. \[InvisibleSpace]bulksol\) /. cNQMval\) /. cRval]], {i, 1, travi}], TableDepth \[Rule] 2, TableAlignments \[Rule] Center]\)], "Input"], Cell[BoxData[ TagBox[GridBox[{ {"\<\"trave 1\"\>", "0"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Center}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Center]]]], "Output"] }, Open ]] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Dati numerici [", StyleBox["D5", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell["\<\ Sono assegnati valori numerici alle rigidezze e ai parametri che descrivono \ le forse attive.\ \>", "Text"], Cell[BoxData[ \(\(datip = {\[ScriptB] \[Rule] 100, \[ScriptCapitalY]\[ScriptCapitalJ] \[Rule] 10, \[Kappa] \[Rule] 0.1};\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell["\<\ Potrebbe essere necessario assegnare dei valori (arbitrari) ai coefficienti \ cA[i] per selezionare una delle molteplici soluzioni Sono assegnati automaticamente dei valori nulli ai coefficienti A[i] \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(cAval0 = If[Length[cRnull] > 0, Table[cA[i] \[Rule] 0, {i, 1, Length[cRnull]}], {}]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell["\<\ Se si vogliono assegnare altri valori, farlo qui. Altrimenti assegnare una \ lista vuota: iAval={}\ \>", "Text"], Cell[BoxData[ \(\(cAval = {};\)\)], "Input", CellFrame->True, Background->GrayLevel[0.849989]], Cell[CellGroupData[{ Cell[BoxData[ \(cAval1 = If[\((Length[cRnull] > 0)\) && \((Length[cAval] == Length[cRnull])\), cAval, cAval0]\)], "Input"], Cell[BoxData[ \({}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(datinum = Join[datiO, datip, cAval1]\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalL] \[Rule] 1, \[ScriptB] \[Rule] 100, \[ScriptCapitalY]\[ScriptCapitalJ] \[Rule] 10, \[Kappa] \[Rule] 0.1`}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["\<\ Visualizzazione delle soluzioni (N, Q, M) (u, v, \[Theta])\ \>", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Definizioni", "Subsection"], Cell[BoxData[ \(\(sNQM[ i_]\)[\[Zeta]_] := \(\({\(sN[i]\)[\[Zeta]], \(sQ[ i]\)[\[Zeta]], \(sM[i]\)[\[Zeta]]} /. bulksol\) /. cNQMval\) /. cRval // Simplify\)], "Input"], Cell[BoxData[ \(\(spuv\[Theta][ i_]\)[\[Zeta]_] := \(\({\(u\_1[i]\)[\[Zeta]], \(u\_2[ i]\)[\[Zeta]], \(\[Theta][i]\)[\[Zeta]]} /. vinBer\) /. spsol\) /. cRval\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Eventuali valutazioni ", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(\(spuv\[Theta][1]\)[0] // Simplify\)], "Input"], Cell[BoxData[ \({\(\[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(\@2\ \((8\ \ \[ScriptCapitalY]\[ScriptCapitalJ] + 24\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \[Kappa])\)\), \(-\(\(\[ScriptB]\ \[ScriptCapitalL]\^4\ \[Kappa]\)\/\(8\ \@2\ \ \((\[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Kappa])\)\)\)\), \ \(\[ScriptB]\ \[ScriptCapitalL]\^3\ \((1 + 12\ \[Kappa])\)\)\/\(48\ \@2\ \((\ \[ScriptCapitalY]\[ScriptCapitalJ] + 3\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \ \[Kappa])\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(spuv\[Theta][1]\)[L[1]] // Factor\)], "Input"], Cell[BoxData[ \({0, 0, 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(spuv\[Theta][2]\)[0] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\(u\_1[2]\)[0]\), ",", \(\(u\_2[2]\)[0]\), ",", RowBox[{ SuperscriptBox[\(u\_2[2]\), "\[Prime]", MultilineFunction->None], "[", "0", "]"}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(spuv\[Theta][2]\)[L[2]] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{\(\(u\_1[2]\)[L[2]]\), ",", \(\(u\_2[2]\)[L[2]]\), ",", RowBox[{ SuperscriptBox[\(u\_2[2]\), "\[Prime]", MultilineFunction->None], "[", \(L[2]\), "]"}]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(sNQM[1]\)[0] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ \({\(3\ \[ScriptB]\ \[ScriptCapitalL]\ \((1 + 4\ \[Kappa])\)\)\/\(8\ \@2\ \ \((1 + 3\ \[Kappa])\)\), \(3\ \[ScriptB]\ \[ScriptCapitalL]\ \((1 + 4\ \ \[Kappa])\)\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\), 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(sNQM[1]\)[L[1]] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ \({\(-\(\(\[ScriptB]\ \[ScriptCapitalL]\ \((5 + 12\ \[Kappa])\)\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\)\)\), \(-\(\(\[ScriptB]\ \[ScriptCapitalL]\ \ \((5 + 12\ \[Kappa])\)\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\)\)\), \(\[ScriptB]\ \ \[ScriptCapitalL]\^2\)\/\(8\ \@2\ \((1 + 3\ \[Kappa])\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(sNQM[2]\)[0] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ \({\(sN[2]\)[0], \(sQ[2]\)[0], \(sM[2]\)[0]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(sNQM[2]\)[L[2]] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ \({\(sN[2]\)[L[2]], \(sQ[2]\)[L[2]], \(sM[2]\)[L[2]]}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Funzioni per la visualizzazione", "Subsection", Evaluatable->False], Cell[TextData[{ "Assegnare a ", StyleBox["ticksOption ", FontFamily->"Courier", FontWeight->"Bold"], " ", StyleBox["Automatic", FontFamily->"Courier", FontWeight->"Bold"], " per avere gli assi graduati, ", StyleBox["None;", FontFamily->"Courier", FontWeight->"Bold"], " altrimenti" }], "SmallText", CellFrame->False, Background->None], Cell[TextData[{ "Adattare ", StyleBox["PlotRange ", FontFamily->"Courier", FontWeight->"Bold"], "o lasciare ", StyleBox["All", FontFamily->"Courier", FontWeight->"Bold"], " " }], "SmallText", CellFrame->False, Background->None], Cell[BoxData[ RowBox[{\(grNQM[it_]\), ":=", RowBox[{"GraphicsArray", "[", RowBox[{ RowBox[{"{", RowBox[{"Table", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{\(Evaluate[{0, \(\(sNQM[ it]\)[\[Zeta]]\)\[LeftDoubleBracket] i\[RightDoubleBracket] /. datinum // Simplify}]\), ",", \(Evaluate[{\[Zeta], 0, L[it]} /. datinum]\), ",", \(DisplayFunction \[Rule] Identity\), ",", \(Ticks \[Rule] ticksOption\), ",", \(PlotRange \[Rule] {All, All, All}\_\(\(\ \[LeftDoubleBracket]\)\(i\)\(\[RightDoubleBracket]\)\)\), ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"{", RowBox[{\(Thickness[0.004]\), ",", SubscriptBox[ RowBox[{"{", RowBox[{\(Hue[0.5]\), ",", \(Hue[0.6]\), ",", FormBox[\(Hue[0.85]\), "TraditionalForm"]}], "}"}], \(\(\[LeftDoubleBracket]\)\(i\)\(\ \[RightDoubleBracket]\)\)]}], "}"}]}], "}"}]}]}], "]"}], ",", \({i, 1, 3}\)}], "]"}], "}"}], ",", \(GraphicsSpacing \[Rule] 0.4\)}], "]"}]}]], "Input"], Cell[BoxData[ RowBox[{\(gruv\[Theta][it_]\), ":=", RowBox[{"GraphicsArray", "[", RowBox[{ RowBox[{"{", RowBox[{"Table", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{\(Evaluate[{0, \(\(spuv\[Theta][ it]\)[\[Zeta]]\)\[LeftDoubleBracket] i\[RightDoubleBracket] /. datinum // Simplify}]\), ",", \(Evaluate[{\[Zeta], 0, L[it]} /. datinum]\), ",", \(DisplayFunction \[Rule] Identity\), ",", \(Ticks \[Rule] ticksOption\), ",", \(PlotRange \[Rule] {All, All, All}\_\(\(\ \[LeftDoubleBracket]\)\(i\)\(\[RightDoubleBracket]\)\)\), ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"{", RowBox[{\(Thickness[0.004]\), ",", SubscriptBox[ RowBox[{"{", RowBox[{ FormBox[\(Hue[0.15]\), "TraditionalForm"], ",", \(Hue[0.10]\), ",", \(Hue[0.22]\)}], "}"}], \(\(\[LeftDoubleBracket]\)\(i\)\(\ \[RightDoubleBracket]\)\)]}], "}"}]}], "}"}]}]}], "]"}], ",", \({i, 1, 3}\)}], "]"}], "}"}], ",", \(GraphicsSpacing \[Rule] 0.3\)}], "]"}]}]], "Input"], Cell[TextData[{ "Assegnare a ", StyleBox["ticksOption ", FontFamily->"Courier", FontWeight->"Bold"], " ", StyleBox["Automatic", FontFamily->"Courier", FontWeight->"Bold"], " per avere gli assi graduati, ", StyleBox["None;", FontFamily->"Courier", FontWeight->"Bold"], " altrimenti" }], "Text", CellFrame->True, Background->GrayLevel[0.849989]], Cell[BoxData[ \(\(ticksOption = {None, None};\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Grafici dei descrittori della tensione (N, Q, M)", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(Do[Show[grNQM[it], ImageSize \[Rule] {420, Automatic}], {it, 1, travi}]\)], "Input", CellOpen->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .16264 %%ImageSize: 420 68.309 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.31746 0.00387239 0.31746 [ [ 0 0 0 0 ] [ 1 .16264 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .16264 L 0 .16264 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00387239 0.274436 0.158768 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.365614 0.00832412 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .36561 m 1 .36561 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .36561 m .06244 .36561 L .10458 .36561 L .14415 .36561 L .18221 .36561 L .22272 .36561 L .26171 .36561 L .30316 .36561 L .34309 .36561 L .3815 .36561 L .42237 .36561 L .46172 .36561 L .49955 .36561 L .53984 .36561 L .57861 .36561 L .61984 .36561 L .65954 .36561 L .69774 .36561 L .73838 .36561 L .77751 .36561 L .81909 .36561 L .85916 .36561 L .89771 .36561 L .93871 .36561 L .97619 .36561 L s 0 1 1 r .004 w .02381 .60332 m .06244 .57944 L .10458 .5534 L .14415 .52894 L .18221 .50542 L .22272 .48039 L .26171 .45629 L .30316 .43067 L .34309 .406 L .3815 .38225 L .42237 .357 L .46172 .33268 L .49955 .30929 L .53984 .2844 L .57861 .26043 L .61984 .23495 L .65954 .21041 L .69774 .18681 L .73838 .16169 L .77751 .13751 L .81909 .11181 L .85916 .08704 L .89771 .06322 L .93871 .03788 L .97619 .01472 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.374687 0.00387239 0.625313 0.158768 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.365614 0.00832412 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .36561 m 1 .36561 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .36561 m .06244 .36561 L .10458 .36561 L .14415 .36561 L .18221 .36561 L .22272 .36561 L .26171 .36561 L .30316 .36561 L .34309 .36561 L .3815 .36561 L .42237 .36561 L .46172 .36561 L .49955 .36561 L .53984 .36561 L .57861 .36561 L .61984 .36561 L .65954 .36561 L .69774 .36561 L .73838 .36561 L .77751 .36561 L .81909 .36561 L .85916 .36561 L .89771 .36561 L .93871 .36561 L .97619 .36561 L s 0 .4 1 r .004 w .02381 .60332 m .06244 .57944 L .10458 .5534 L .14415 .52894 L .18221 .50542 L .22272 .48039 L .26171 .45629 L .30316 .43067 L .34309 .406 L .3815 .38225 L .42237 .357 L .46172 .33268 L .49955 .30929 L .53984 .2844 L .57861 .26043 L .61984 .23495 L .65954 .21041 L .69774 .18681 L .73838 .16169 L .77751 .13751 L .81909 .11181 L .85916 .08704 L .89771 .06322 L .93871 .03788 L .97619 .01472 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.725564 0.00387239 0.97619 0.158768 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.284823 0.0468438 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .28482 m 1 .28482 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .28482 m .06244 .28482 L .10458 .28482 L .14415 .28482 L .18221 .28482 L .22272 .28482 L .26171 .28482 L .30316 .28482 L .34309 .28482 L .3815 .28482 L .42237 .28482 L .46172 .28482 L .49955 .28482 L .53984 .28482 L .57861 .28482 L .61984 .28482 L .65954 .28482 L .69774 .28482 L .73838 .28482 L .77751 .28482 L .81909 .28482 L .85916 .28482 L .89771 .28482 L .93871 .28482 L .97619 .28482 L s 1 0 .9 r .004 w .02381 .28482 m .06244 .23328 L .10458 .18329 L .14415 .14224 L .18221 .10816 L .22272 .07769 L .26171 .05402 L .28158 .04409 L .30316 .03495 L .32216 .0283 L .34309 .02251 L .36292 .0185 L .37378 .01691 L .38395 .01581 L .38891 .01541 L .39154 .01524 L .39433 .01508 L .39702 .01495 L .39945 .01486 L .40062 .01483 L .40189 .01479 L .40309 .01477 L .4042 .01475 L .40528 .01473 L .40644 .01472 L .40772 .01472 L .40889 .01472 L .41011 .01472 L .4108 .01472 L .41144 .01473 L .4126 .01475 L .41385 .01477 L .41602 .01482 L .41807 .01488 L .42272 .01509 L .42742 .01537 L .43256 .01578 L .44291 .01689 L .45249 .01826 L .46141 .01984 L .48187 .02456 L .50046 .03018 L .54044 .04654 L .5789 .06778 L .61982 .09631 L .65923 .12957 L .69711 .16689 L .73745 .21239 L .77628 .26179 L .81755 .32035 L Mistroke .85731 .38264 L .89556 .44801 L .93626 .52343 L .97544 .60176 L .97619 .60332 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{420, 68.25}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGoo000?Ool00`00Oomoo`1DOol20olhOol00`00Oomoo`1DOol20IlhOol00`00Oomoo`0AOol0 0g`LOomoo`0SOol00g`LOomoo`0fOol000moo`03001oogoo05=oo`030omoogoo03Qoo`03001oogoo 05=oo`030Imoogoo03Qoo`03001oogoo011oo`03O1aoogoo02Eoo`9l73Ioo`003goo00<007ooOol0 DGoo0P?o>goo00<007ooOol0DGoo0P6O>goo00<007ooOol03Woo0W`L:Woo00=l77ooOol0Ool00g`LOomoo`0OOol000moo`03 001oogoo02ioo`030omoogoo05eoo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo04ioo`03 O1aoogoo01moo`003goo00<007ooOol0;7oo0P?oH7oo00<007ooOol0;7oo0P6OH7oo00<007ooOol0 Cgoo00=l77ooOol07Woo000?Ool00`00Oomoo`0ZOol20omROol00`00Oomoo`0ZOol20ImROol00`00 Oomoo`1@Ool00g`LOomoo`0MOol000moo`03001oogoo02Uoo`030omoogoo069oo`03001oogoo02Uo o`030Imoogoo069oo`03001oogoo051oo`03O1aoogoo01eoo`003goo00<007ooOol09goo0P?oIGoo 00<007ooOol09goo0P6OIGoo00<007ooOol0DGoo00=l77ooOol077oo000?Ool00`00Oomoo`0VOol0 0`?oOomoo`1UOol00`00Oomoo`0VOol00`6OOomoo`1UOol00`00Oomoo`1AOol00g`LOomoo`0LOol0 00aoobX00083ocd002QoobX00081Wcd002]oo`03001oogoo059oo`03O1aoogoo01]oo`003goo00<0 07ooOol08Woo0P?oJWoo00<007ooOol08Woo0P6OJWoo00<007ooOol0DWoo00=l77ooOol06goo000? Ool00`00Oomoo`0QOol00`?oOomoo`1ZOol00`00Oomoo`0QOol00`6OOomoo`1ZOol00`00Oomoo`1C Ool00g`LOomoo`0JOol000moo`03001oogoo01moo`83ofeoo`03001oogoo01moo`81Wfeoo`03001o ogoo05Aoo`03O1aoogoo01Uoo`003goo00<007ooOol07Woo00<3ogooOol0KGoo00<007ooOol07Woo 00<1WgooOol0KGoo00<007ooOol0E7oo00=l77ooOol06Goo000?Ool00`00Oomoo`0LOol20om`Ool0 0`00Oomoo`0MOol00`6OOomoo`1^Ool00`00Oomoo`1EOol00g`LOomoo`0HOol000moo`03001oogoo 01Yoo`83og9oo`03001oogoo01]oo`81Wg5oo`03001oogoo05Ioo`03O1aoogoo01Moo`003goo00<0 07ooOol06Goo00<3ogooOol0LWoo00<007ooOol06Goo0P6OLgoo00<007ooOol0EWoo00=l77ooOol0 5goo000?Ool00`00Oomoo`0GOol20omeOol00`00Oomoo`0GOol20ImeOol00`00Oomoo`1GOol00g`L Oomoo`0FOol000moo`03001oogoo01Eoo`83ogMoo`03001oogoo01Eoo`81WgMoo`03001oogoo05Mo o`03O1aoogoo01Ioo`003goo00<007ooOol057oo00<3ogooOol0Mgoo00<007ooOol057oo00<1Wgoo Ool0Mgoo00<007ooOol0F7oo00=l77ooOol05Goo000?Ool00`00Oomoo`0BOol20omjOol00`00Oomo o`0BOol20ImjOol00`00Oomoo`1HOol00g`LOomoo`0EOol000moo`03001oogoo015oo`030omoogoo 07Yoo`03001oogoo015oo`030Imoogoo07Yoo`03001oogoo05Uoo`03O1aoogoo01Aoo`003goo00<0 07ooOol03goo0P?oOGoo00<007ooOol03goo0P6OOGoo00<007ooOol0FGoo00=l77ooOol057oo000? Ool00`00Oomoo`0=Ool20omoOol00`00Oomoo`0=Ool20ImoOol00`00Oomoo`1JOol00g`LOomoo`0C Ool000moo`03001oogoo00aoo`030omoogoo07moo`03001oogoo00aoo`030Imoogoo07moo`03001o ogoo05Yoo`03O1aoogoo01=oo`003goo00<007ooOol02Woo0P?oPWoo00<007ooOol02Woo0P6OPWoo 00<007ooOol0Fgoo00=l77ooOol04Woo000?Ool00`00Oomoo`09Ool00`?oOomoo`22Ool00`00Oomo o`09Ool00`6OOomoo`22Ool00`00Oomoo`1KOol00g`LOomoo`0BOol000moo`03001oogoo00Moo`83 ohEoo`03001oogoo00Moo`81WhEoo`03001oogoo05aoo`03O1aoogoo015oo`003goo00<007ooOol0 1Goo0P?oQgoo00<007ooOol01Goo0P6OQgoo00<007ooOol0G7oo00=l77ooOol04Goo000?Ool00`00 Oomoo`04Ool00`?oOomoo`27Ool00`00Oomoo`04Ool00`6OOomoo`27Ool00`00Oomoo`1MOol00g`L Oomoo`0@Ool000moo`03001oogoo009oo`83ohYoo`03001oogoo009oo`81WhYoo`03001oogoo05eo o`03O1aoogoo011oo`003goo00D007ooOomoo`?o08aoo`05001oogooOol1W`2Ool000moo`03001o ogoo08ioo`03001oogoo08ioo`03001oogoo071oo`003goo00<007ooOol0SWoo00<007ooOol0SWoo 00<007ooOol0L7oo003oOonUOol00001\ \>"], ImageRangeCache->{{{0, 419}, {67.25, 0}} -> {-0.0960041, -0.0122006, \ 0.00761817, 0.00761817}, {{12.5625, 116.188}, {65.625, 1.5625}} -> \ {-0.152298, -45.8176, 0.0101328, 1.15931}, {{157.625, 261.313}, {65.625, \ 1.5625}} -> {-1.62187, -45.8059, 0.0101298, 1.15897}, {{302.75, 406.375}, \ {65.625, 1.5625}} -> {-3.09271, -6.41707, 0.0101328, 0.20601}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Grafici dello spostamento (u, v, \[Theta])\ \>", "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(\(Do[ Show[gruv\[Theta][it], ImageSize \[Rule] {420, Automatic}], {it, 1, travi}];\)\)], "Input", CellOpen->False], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .17168 %%ImageSize: 420 72.104 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.31746 0.00408753 0.31746 [ [ 0 0 0 0 ] [ 1 .17168 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .17168 L 0 .17168 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00408753 0.28836 0.167589 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 4.68437 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .01472 m 1 .01472 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .01472 m .06244 .01472 L .10458 .01472 L .14415 .01472 L .18221 .01472 L .22272 .01472 L .26171 .01472 L .30316 .01472 L .34309 .01472 L .3815 .01472 L .42237 .01472 L .46172 .01472 L .49955 .01472 L .53984 .01472 L .57861 .01472 L .61984 .01472 L .65954 .01472 L .69774 .01472 L .73838 .01472 L .77751 .01472 L .81909 .01472 L .85916 .01472 L .89771 .01472 L .93871 .01472 L .97619 .01472 L s 1 .9 0 r .004 w .02381 .33321 m .06244 .38475 L .10458 .43475 L .14415 .4758 L .18221 .50988 L .22272 .54035 L .26171 .56402 L .28158 .57394 L .30316 .58308 L .32216 .58973 L .34309 .59552 L .36292 .59954 L .37378 .60113 L .38395 .60223 L .38891 .60262 L .39154 .6028 L .39433 .60296 L .39702 .60308 L .39945 .60317 L .40062 .60321 L .40189 .60324 L .40309 .60327 L .4042 .60329 L .40528 .6033 L .40644 .60331 L .40772 .60332 L .40889 .60332 L .41011 .60331 L .4108 .60331 L .41144 .6033 L .4126 .60329 L .41385 .60327 L .41602 .60321 L .41807 .60315 L .42272 .60295 L .42742 .60266 L .43256 .60226 L .44291 .60115 L .45249 .59977 L .46141 .59819 L .48187 .59347 L .50046 .58785 L .54044 .5715 L .5789 .55025 L .61982 .52172 L .65923 .48847 L .69711 .45114 L .73745 .40564 L .77628 .35624 L .81755 .29768 L Mistroke .85731 .23539 L .89556 .17002 L .93626 .0946 L .97544 .01627 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.367725 0.00408753 0.632275 0.167589 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.485116 6.91857 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .48512 m 1 .48512 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .48512 m .06244 .48512 L .10458 .48512 L .14415 .48512 L .18221 .48512 L .22272 .48512 L .26171 .48512 L .30316 .48512 L .34309 .48512 L .3815 .48512 L .42237 .48512 L .46172 .48512 L .49955 .48512 L .53984 .48512 L .57861 .48512 L .61984 .48512 L .65954 .48512 L .69774 .48512 L .73838 .48512 L .77751 .48512 L .81909 .48512 L .85916 .48512 L .89771 .48512 L .93871 .48512 L .97619 .48512 L s 1 .6 0 r .004 w .02381 .01472 m .06244 .08447 L .10458 .15909 L .14415 .22654 L .18221 .28799 L .22272 .34883 L .26171 .40218 L .30316 .45262 L .34309 .49462 L .3815 .52862 L .42237 .55771 L .44268 .56944 L .46172 .5788 L .48111 .58673 L .49955 .59279 L .50923 .5954 L .5198 .59781 L .52934 .59961 L .53832 .60097 L .54328 .60158 L .54864 .60214 L .5531 .60252 L .558 .60285 L .56056 .60299 L .56331 .60311 L .56483 .60317 L .56621 .60321 L .56762 .60325 L .56892 .60327 L .57012 .60329 L .57139 .60331 L .57267 .60332 L .5734 .60332 L .57408 .60332 L .57531 .60332 L .57643 .60331 L .57767 .60329 L .57897 .60327 L .5802 .60325 L .58154 .60322 L .58397 .60314 L .58851 .60295 L .59382 .60263 L .59871 .60225 L .60763 .60136 L .61708 .60014 L .63665 .59673 L .65496 .59255 L .69379 .58094 L .73507 .56537 L Mistroke .77483 .54839 L .81307 .53144 L .85377 .51421 L .89295 .49996 L .91296 .4941 L .92349 .49151 L .93459 .48921 L .94456 .48753 L .94984 .48681 L .95549 .48618 L .9607 .48572 L .96543 .48541 L .96772 .4853 L .96892 .48525 L .9702 .48521 L .97131 .48518 L .97254 .48515 L .97366 .48513 L .9747 .48512 L .97548 .48512 L .97619 .48512 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.71164 0.00408753 0.97619 0.167589 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.130707 1.89575 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .13071 m 1 .13071 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .13071 m .06244 .13071 L .10458 .13071 L .14415 .13071 L .18221 .13071 L .22272 .13071 L .26171 .13071 L .30316 .13071 L .34309 .13071 L .3815 .13071 L .42237 .13071 L .46172 .13071 L .49955 .13071 L .53984 .13071 L .57861 .13071 L .61984 .13071 L .65954 .13071 L .69774 .13071 L .73838 .13071 L .77751 .13071 L .81909 .13071 L .85916 .13071 L .89771 .13071 L .93871 .13071 L .97619 .13071 L s .68 1 0 r .004 w .02381 .60332 m .02499 .60331 L .02605 .6033 L .02729 .60328 L .02846 .60325 L .03053 .60318 L .03279 .60308 L .03527 .60293 L .0379 .60273 L .04262 .60228 L .05205 .601 L .06244 .59901 L .07293 .59643 L .0842 .59301 L .10458 .58521 L .1458 .5636 L .18551 .53622 L .22371 .50473 L .26435 .46665 L .30348 .42648 L .34506 .38108 L .38513 .33572 L .42368 .29152 L .46468 .2449 L .50417 .20139 L .54214 .16172 L .58257 .1228 L .62148 .08949 L .66284 .0596 L .68353 .0471 L .70268 .03717 L .72245 .02867 L .74101 .02243 L .75075 .01986 L .75968 .01794 L .76959 .01632 L .7748 .01569 L .77762 .01541 L .78028 .0152 L .78268 .01503 L .78528 .01489 L .78643 .01484 L .78764 .0148 L .78878 .01477 L .78982 .01475 L .79103 .01473 L .79233 .01472 L .79354 .01472 L .79468 .01472 L .79532 .01473 L Mistroke .796 .01474 L .79723 .01477 L .7987 .01481 L .80002 .01486 L .80239 .01498 L .80457 .01511 L .80948 .01553 L .81382 .01603 L .81839 .01667 L .82789 .01845 L .83806 .021 L .85641 .02736 L .87769 .03767 L .89782 .05046 L .93621 .08347 L .97619 .13071 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{420, 72.0625}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00=Gh7ooOol09Woo00=Gh7ooOol03goo000?Ool00`00Oomoo`1NOol00gn0Oomoo`0ZOol00`00 Oomoo`04Ool00giPOomoo`22Oolo00000eOP0000000X000015OP000000003Goo000?Ool00`00Oomo o`1NOol00gn0Oomoo`0ZOol00`00Oomoo`04Ool00giPOomoo`24Ool00`00Oomoo`0iOol00eOPOomo o`0jOol000moo`03001oogoo05eoo`03Oh1oogoo02]oo`03001oogoo00Eoo`03OV1oogoo08=oo`03 001oogoo03Qoo`03En1oogoo03]oo`003goo00<007ooOol0GGoo00=oP7ooOol0:goo00<007ooOol0 1Goo00=nH7ooOol0Pgoo00<007ooOol0=goo00=Gh7ooOol0?7oo000?Ool00`00Oomoo`1LOol00gn0 Oomoo`0/Ool00`00Oomoo`06Ool00giPOomoo`22Ool00`00Oomoo`0fOol00eOPOomoo`0mOol000mo o`03001oogoo05aoo`03Oh1oogoo02aoo`03001oogoo00Moo`03OV1oogoo085oo`03001oogoo03Eo o`03En1oogoo03ioo`003goo00<007ooOol0Fgoo00=oP7ooOol0;Goo00<007ooOol01goo00=nH7oo Ool0PGoo00<007ooOol0=7oo00=Gh7ooOol0?goo000?Ool00`00Oomoo`1KOol00gn0Oomoo`0]Ool0 0`00Oomoo`08Ool00giPOomoo`20Ool00`00Oomoo`0cOol00eOPOomoo`10Ool000moo`03001oogoo 05Yoo`03Oh1oogoo02ioo`03001oogoo00Qoo`03OV1oogoo081oo`03001oogoo039oo`03En1oogoo 045oo`003goo00<007ooOol0FWoo00=oP7ooOol0;Woo00<007ooOol02Goo00=nH7ooOol0Ogoo00<0 07ooOol07oo00<007ooOol04goo 00=nH7ooOol0MGoo00<007ooOol097oo00=Gh7ooOol0Cgoo000?Ool00`00OomoP01?Ool00gn0Oomo o`0iOol00`00Oomoo`0DOol00giPOomoo`1dOol00`00Oomoo`0SOol00eOPOomoo`1@Ool000moo`03 001oogn004ioo`03Oh1oogoo03Yoo`03001oogoo01Aoo`03OV1oogoo07Aoo`03001oogoo029oo`03 En1oogoo055oo`003goo00@007ooOomoP4eoo`03Oh1oogoo03Yoo`03001oogoo01Eoo`03OV1oogoo 07=oo`03001oogoo025oo`03En1oogoo059oo`003goo00D007ooOomoogn004]oo`03Oh1oogoo03]o o`03001oogoo01Ioo`03OV1oogoo079oo`03001oogoo021oo`03En1oogoo05=oo`003goo00<007oo Ool00Woo00=oP7ooOol0Agoo00=oP7ooOol0?7oo00<007ooOol05Woo00=nH7ooOol0LWoo00<007oo Ool07goo00=Gh7ooOol0E7oo000?Ool00`00Oomoo`02Ool00gn0Oomoo`17Ool00gn0Oomoo`0lOol0 0`00Oomoo`0GOol00giPOomoo`1aOol00`00Oomoo`0NOol00eOPOomoo`1EOol000moo`03001oogoo 00=oo`03Oh1oogoo04Eoo`03Oh1oogoo03eoo`03001oogoo01Qoo`03OV1oogoo071oo`03001oogoo 01ioo`03En1oogoo05Eoo`003goo00<007ooOol017oo00=oP7ooOol0@goo00=oP7ooOol0?Woo00<0 07ooOol067oo00=nH7ooOol0L7oo00<007ooOol07Goo00=Gh7ooOol0EWoo000?Ool00`00Oomoo`04 Ool00gn0Oomoo`12Ool00gn0Oomoo`0oOol00`00Oomoo`0IOol00giPOomoo`1_Ool00`00Oomoo`0L Ool00eOPOomoo`1GOol000moo`03001oogoo00Eoo`03Oh1oogoo041oo`03Oh1oogoo041oo`03001o ogoo01Yoo`03OV1oogoo06ioo`03001oogoo01]oo`03En1oogoo05Qoo`003goo00<007ooOol01Woo 00=oP7ooOol0?Woo00=oP7ooOol0@Goo00<007ooOol06Woo00=nH7ooOol0KWoo00<007ooOol06Woo 00=Gh7ooOol0FGoo000?Ool00`00Oomoo`07Ool2Oh0mOol00gn0Oomoo`12Ool00`00Oomoo`0KOol0 0giPOomoo`1]Ool00`00Oomoo`0IOol00eOPOomoo`1JOol000moo`03001oogoo00Uoo`03Oh1oogoo 03Uoo`03Oh1oogoo04=oo`03001oogoo01aoo`03OV1oogoo06aoo`03001oogoo01Qoo`03En1oogoo 05]oo`003goo00<007ooOol02Woo00=oP7ooOol0=goo00=oP7ooOol0A7oo00<007ooOol07Goo0WiP K7oo00<007ooOol05goo00=Gh7ooOol0G7oo000?Ool00`00Oomoo`0;Ool00gn0Oomoo`0eOol00gn0 Oomoo`12OolU00000giP000000100004OV03000ROol00`00Oomoo`0EOol2En1OOol000moo`03001o ogoo00aoo`03Oh1oogoo03=oo`03Oh1oogoo04Ioo`03001oogoo021oo`03OV1oogoo03]oo`EnH2Qo o`03001oogoo01Aoo`03En1oogoo05moo`003goo00<007ooOol03Goo00=oP7ooOol0Ool00gn0Oomoo`0^Ool2Oh1:Ool00`00Oomoo`0ROol00giPOomoo`0bOol4 OV0`Ool00`00Oomoo`0BOol00eOPOomoo`1QOol000moo`03001oogoo00moo`03Oh1oogoo02aoo`03 Oh1oogoo04Yoo`03001oogoo02=oo`03OV1oogoo02moo`9nH3Aoo`03001oogoo015oo`03En1oogoo 069oo`003goo00<007ooOol047oo0Wn0:Woo0Wn0CGoo00<007ooOol097oo00=nH7ooOol0;7oo0WiP =Woo00<007ooOol047oo00=Gh7ooOol0Hgoo000?Ool00`00Oomoo`0BOol00gn0Oomoo`0UOol2Oh1? Ool00`00Oomoo`0UOol2OV0ZOol2OV0hOol00`00Oomoo`0?Ool00eOPOomoo`1TOol000moo`03001o ogoo01=oo`9oP2Aoo`03Oh1oogoo04moo`03001oogoo02Moo`9nH2Ioo`9nH3Yoo`03001oogoo00io o`03En1oogoo06Eoo`003goo00<007ooOol05Goo0Wn08Goo00=oP7ooOol0D7oo00<007ooOol0:Goo 00=nH7ooOol08Goo0WiP?7oo00<007ooOol037oo0UOPJ7oo000?Ool00`00Oomoo`0GOol00gn0Oomo o`0LOol2Oh1COol00`00Oomoo`0ZOol2OV0NOol3OV0nOol00`00Oomoo`0:Ool2En1ZOol000moo`03 001oogoo01Qoo`9oP1]oo`03Oh1oogoo05=oo`03001oogoo02aoo`03OV1oogoo01Uoo`9nH45oo`03 001oogoo00Qoo`9Gh6aoo`003goo00<007ooOol06Woo0Wn05goo0Wn0EWoo00<007ooOol0;Goo0giP 5Goo0giP@goo00<007ooOol01Woo0UOPKWoo000?Ool00`00Oomoo`0LOol5Oh0=Ool5Oh1HOol00`00 Oomoo`0`Ool3OV0=Ool5OV16Ool00`00Oomoo`03Ool3En1`Ool000moo`03001oogoo025oo`eoP5eo o`03001oogoo03=oo`enH4]oo`IGh7=oo`003goo00<007ooOol0Rgoo00<007ooOol0Rgoo00<007oo Ool0MWoo000?Ool00`00Oomoo`2;Ool00`00Oomoo`2;Ool00`00Oomoo`1fOol00?moojEoo`00\ \>"], ImageRangeCache->{{{0, 419}, {71.0625, 0}} -> {-0.0943298, -0.0128784, \ 0.00761017, 0.00761017}, {{12.375, 121.875}, {69.3125, 1.6875}} -> {-0.14414, \ -0.00655621, 0.00959613, 0.00195099}, {{154.75, 264.25}, {69.3125, 1.6875}} -> \ {-1.51039, -0.0724301, 0.00959613, 0.00132096}, {{297.063, 406.563}, \ {69.3125, 1.6875}} -> {-2.87604, -0.0773855, 0.00959613, 0.00482087}}] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Visualizzazione della deformazione [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Definizioni per la visualizzazione", "Subsection"], Cell["\<\ Si vedano anche le definizioni gi\[AGrave] date per realizzare il disegno \ della configurazione originaria\ \>", "SmallText"], Cell[BoxData[ \(\(asseD[ i_]\)[\[Zeta]_] := \(\(org[i] + a\_1[i] \[Zeta] + \(u[ i]\)[\[Zeta]] /. \[InvisibleSpace]spsol\) \ /. \[InvisibleSpace]cRval\) /. datinum\)], "Input"], Cell[BoxData[ \(\(secD[ i_]\)[\[Zeta]_] := \(\(\({\(asseD[i]\)[\[Zeta]] - maxL\/20\ \((\(-\(\[Theta][i]\)[\[Zeta]]\)\ a\_1[i] + a\_2[i])\)\ , \(asseD[i]\)[\[Zeta]] + maxL\/20\ \((\(-\(\[Theta][i]\)[\[Zeta]]\)\ a\_1[i] + a\_2[i])\)\ } /. \[InvisibleSpace]vinBer\) \ /. \[InvisibleSpace]spsol\) /. \[InvisibleSpace]cRval\) /. datinum\)], "Input"], Cell["disegno dell'asse", "SmallText"], Cell[BoxData[ \(\(pltD = ParametricPlot[ Evaluate[ Flatten[Table[{\(asseD[i]\)[L[i]\ \[Xi]]}, {i, 1, travi}], 1]], {\[Xi], 0, 1}, Axes \[Rule] False, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotStyle \[Rule] Hue[1]];\)\)], "Input"], Cell["disegno delle sezioni", "SmallText"], Cell[BoxData[ \(\(pltDs = Table[Table[ Graphics[{Hue[1], Line[\(secD[i]\)[j \(\(\ \)\(L[i]\)\)\/ndiv]]}], {j, 1, ndiv - 1}], {i, 1, travi}] // Flatten;\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(pltDv = Block[{asseO = asseD}, vincoliFig /. datinum]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], ",", TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]}], "}"}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(pltDbv = Block[{asseO = asseD}, vincolibFig /. datinum]\)], "Input"], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False], ",", TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]}], "}"}]], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Definizione cornice ", "Subsection"], Cell["\<\ Serve per ottenere figure confrontabili. Scegliere i parametri in modo che la \ figura sia contenuta nel rettangolo di sfondo. Verificare che anche i \ diagrammi N Q M risultino contenuti nel rettangolo.\ \>", "SmallText"], Cell[CellGroupData[{ Cell[BoxData[ \(xMax = Max /@ N[Transpose[ Flatten[Table[{\(asseO[i]\)[0], \(asseO[i]\)[ L[i]], \(asseD[i]\)[0], \(asseD[i]\)[L[i]]}, {i, 1, travi}], 1]] /. \[InvisibleSpace]datinum]\)], "Input"], Cell[BoxData[ \({0.`, 0.`}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(xMin = Min /@ N[Transpose[ Flatten[Table[{\(asseO[i]\)[0], \(asseO[i]\)[ L[i]], \(asseD[i]\)[0], \(asseD[i]\)[L[i]]}, {i, 1, travi}], 1]] /. \[InvisibleSpace]datinum]\)], "Input"], Cell[BoxData[ \({\(-0.7071067811865476`\), \(-0.7071067811865476`\)}\)], "Output"] }, Open ]], Cell[BoxData[ \(xDiag := \((xMax - xMin)\) + \((e\_1 + e\_2)\)\ 0.001\)], "Input"], Cell[BoxData[{ \(\(xLowerL := xC - mU . \(xDiag\/2\);\)\), "\n", \(\(xUpperR := xC + mU . \(xDiag\/2\);\)\)}], "Input"], Cell[BoxData[ \(\(frameb := Graphics[{GrayLevel[0.9], Rectangle[xLowerL, xUpperR]}];\)\)], "Input"], Cell[BoxData[ \(\(frame := Graphics[{GrayLevel[0], {Point[xLowerL], Point[xUpperR]}}];\)\)], "Input"], Cell[BoxData[ \(xC := \(xMax + xMin\)\/2 + xCshift\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Adattamento cornice [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "] " }], "Subsection"], Cell["\<\ Il rettangolo di sfondo risulta definito dalla posizione del centro e dalla \ dilatazione dei lati\ \>", "SmallText", CellFrame->True, Background->GrayLevel[0.849989]], Cell[CellGroupData[{ Cell[BoxData[ \(xCshift = 0.02 \(\@\( xDiag . xDiag\)\) \((e\_2)\)\)], "Input"], Cell[BoxData[ \({0, 0.020028284271247462`}\)], "Output"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"mU", "=", RowBox[{"(", GridBox[{ {"1.4", "0"}, {"0", "1.4"} }], ")"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \({\((xUpperR - xLowerL)\), xC}\)], "Input"], Cell[BoxData[ \({{0.9913494936611665`, 0.9913494936611665`}, {\(-0.3535533905932738`\), \ \(-0.3335251063220263`\)}}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Figura", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[frameb, frame, pltO, pltOs, pltOax, pltObv, pltD, pltDs, pltDbv, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic, PlotRange \[Rule] All];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.00293 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.839656 0.960691 0.823277 0.960691 [ [ 0 0 0 0 ] [ 1 1.00293 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .02667 m .02381 .97905 L .97619 .97905 L .97619 .02667 L F 0 g .008 w .02381 .02667 Mdot .97619 .97905 Mdot 2 Mabswid [ ] 0 setdash .83966 .82328 m .16034 .14397 L s .5 Mabswid .63586 .68741 m .70379 .61948 L s .46603 .51759 m .53397 .44966 L s .29621 .34776 m .36414 .27983 L s 0 0 0 r .5 .48362 m .36414 .34776 L s .43207 .3704 m .36414 .34776 L s .38678 .41569 m .36414 .34776 L s .5 .48362 m .63586 .34776 L s .61322 .41569 m .63586 .34776 L s .56793 .3704 m .63586 .34776 L s 0 g 1 Mabswid .08029 .14397 m .2404 .14397 L s .16034 .02388 m .16034 .26405 L s newpath .16034 .14397 .03843 0 365.73 arc s .91971 .82328 m .7596 .82328 L s .83966 .94336 m .83966 .70319 L s newpath .83966 .82328 .03843 0 365.73 arc s 1 0 0 r .5 Mabswid .74728 .82328 m .7191 .7814 L .68912 .73677 L .66157 .69596 L .63551 .65784 L .60817 .61856 L .58217 .58207 L .55479 .54479 L .52863 .51038 L .50363 .47871 L .4772 .44656 L .4519 .41712 L .42773 .39021 L .40219 .36303 L .37784 .33826 L .35225 .31337 L .32797 .29073 L .30504 .27011 L .28118 .24931 L .25887 .2303 L .23599 .21103 L .2149 .19323 L .19567 .17667 L .17651 .15947 L .16034 .14397 L s .54201 .6098 m .62206 .55399 L s .39214 .42252 m .46276 .35728 L s .24931 .28535 m .31339 .21357 L s 0 g 1 Mabswid .08029 .14397 m .2404 .14397 L s .16034 .02388 m .16034 .26405 L s newpath .16034 .14397 .03843 0 365.73 arc s .82734 .82328 m .66722 .82328 L s .74728 .94336 m .74728 .70319 L s newpath .74728 .82328 .03843 0 365.73 arc s 0 0 m 1 0 L 1 1.00293 L 0 1.00293 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 288.813}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL02EcW003001cW7>L0>McW0Qoo`001Woo:7>L00<007>LLi`0 ig>L27oo0006OolXLi`00`00LiacW03WLi`8Ool000IoobQcW003001cW7>L0>McW0Qoo`001Woo:7>L 00<007>LLi`0ig>L27oo0006OolXLi`00`00LiacW03WLi`8Ool000IoobQcW003001cW7>L0>McW0Qo o`001Woo:7>L00<007>LLi`0ig>L27oo0006OolXLi`00`00LiacW03WLi`8Ool000IoobQcW003001c W7>L0>McW0Qoo`001Woo:7>L00<007>LLi`0ig>L27oo0006OolXLi`00`00LiacW03WLi`8Ool000Io obQcW003001cW7>L0>McW0Qoo`001Woo:7>L00<007>LLi`0ig>L27oo0006OolXLi`00`00LiacW03W Li`8Ool000IoobQcW003001cW7>L0>McW0Qoo`001Woo:7>L00<007>LLi`0ig>L27oo0006OolXLi`0 0`00LiacW03WLi`8Ool000IoobQcW003001cW7>L0>McW0Qoo`001Woo:7>L00<007>LLi`0ig>L27oo 0006OolXLi`00`00LiacW03WLi`8Ool000IoobQcW003001cW7>L0>McW0Qoo`001Woo9W>L1P00iW>L 27oo0006OolRLi`40002Li`01000LiacW7>L0P00i7>L27oo0006OolQLi`00`00LiacW004Li`00`00 LiacW003Li`00`00LiacW03QLi`8Ool000Ioob1cW003001cW7>L00EcW003001cW7>L00AcW003001c W7>L0>1cW0Qoo`001Woo7g>L00<007>LLi`01W>L00<007>LLi`01G>L00<007>LLi`0gg>L27oo0006 OolNLi`00`00LiacW007Li`00`00LiacW005Li`00`00LiacW03OLi`8Ool000IooaicW003001cW7>L 00McW003001cW7>L00IcW003001cW7>L0=icW0Qoo`001Woo7G>L00<007>LLi`027>L00<007>LLi`0 1W>L00<007>LLi`0gW>L27oo0006OolMLi`00`00LiacW008Li`00`00LiacW007Li`00`00LiacW03M Li`8Ool000IooaecW003001cW7>L00QcW003001cW7>L00McW003001cW7>L0=ecW0Qoo`001Woo7G>L 00<007>LLi`027>L00<007>LLi`027>L00<007>LLi`0g7>L27oo0006OolALi`_003BLi`8Ool000Io oaecW003001cW7>L00QcW003001l000000McW0800=icW0Qoo`001Woo7G>L00<007>LLi`027>L0P00 00=l0000Li`01G>L00<007>LLi`0gG>L27oo0006OolMLi`00`00LiacW008Li`01@00Li`007`00000 1G>L00<007>LLi`0gG>L27oo0006OolMLi`00`00LiacW008Li`01P00LiacW000O00000AcW003001c W7>L0=ecW0Qoo`001Woo7G>L00<007>LLi`027>L00L007>LLiacW000O0000002Li`00`00LiacW03N Li`8Ool000IooaicW003001cW7>L00McW003001cW7>L009cW005001l0000Li`0003PLi`8Ool000Io oaicW003001cW7>L00McW003001cW7>L00=cW003001l00000>5cW0Qoo`001Woo7g>L00<007>LLi`0 1W>L00<007>LLi`017>L0P0000=l07>LLi`0gW>L27oo0006OolPLi`20006Li`00`00LiacW003Li`0 1@00Li`00000O000gg>L27oo0006OolRLi`20004Li`00`00LiacW0030003Li`200000g`0LiacW03L Li`8Ool000IoobAcW0L000McW0800003O01cW7>L0=]cW0Qoo`001Woo:7>L00<007>LLi`027>L0P00 00=l07>LLi`0fW>L27oo0006OolXLi`00`00LiacW009Li`200000g`0LiacW03ILi`8Ool000IoobQc W003001cW7>L00YcW0800003O01cW7>L0=QcW0Qoo`001Woo:7>L00<007>LLi`02g>L0P0000=l07>L Li`0eg>L27oo0006OolXLi`00`00LiacW00L00ecW080009l0=IcW0Qoo`001Woo:7>L00<007>LLi`03W>L0`0000=l07>LLi`0dg>L27oo0006 OolXLi`00`00LiacW00?Li`300000g`0LiacW03BLi`8Ool000IoobQcW003001cW7>L011cW0<00003 O01cW7>L019cW003O01cW7>L0;acW0Qoo`001Woo:7>L00<007>LLi`04G>L0`0000=l07>LLi`047>L 00=l07>LLi`0_G>L27oo0006OolXLi`00`00LiacW00BLi`30002O00?Li`00g`0LiacW02nLi`8Ool0 00IoobQcW003001cW7>L01=cW0<00003Lial07>L00acW003O01cW7>L0;mcW0Qoo`001Woo:7>L00<0 07>LLi`057>L0`0000=cW7`0Li`02g>L00=l07>LLi`0_g>L27oo0006OolXLi`00`00LiacW00ELi`3 00000g>LO01cW009Li`00g`0LiacW030Li`8Ool000IoobQcW003001cW7>L01IcW0<00003Lial07>L 00McW003O01cW7>L0<5cW0Qoo`001Woo:7>L00<007>LLi`05g>L0`0000=cW7`0Li`01G>L00=l07>L Li`0`W>L27oo0006OolXLi`00`00LiacW00HLi`300000g>LO01l0003Li`00g`0LiacW033Li`8Ool0 00IoobQcW003001cW7>L01UcW0<0009cW003O01cW7`00L00<007>LLi`06W>L 0`000W>L00=l07>LLi`0aG>L27oo0006OolXLi`00`00LiacW00KLi`300000g>LO01l0036Li`8Ool0 00IoobQcW003001cW7>L01acW0800004O01cW7>LO035Li`8Ool000IoobQcW003001cW7>L01ecW003 O0000000009cW09l0<=cW0Qoo`001Woo:7>L00<007>LLi`077>L00=l07>L00000P000g>L00=l07>L Li`0`7>L27oo0006Oom6Li`017`0LiacW7>L0`000g>L00=l07>LLi`0_g>L27oo0006Oom5Li`00g`0 LiacW003Li`30003Li`00g`0LiacW02nLi`8Ool000IoodAcW003O01cW7>L00EcW0<000=cW003O01c W7>L0;ecW0Qoo`001WooA7>L00=l07>LLi`01W>L0`000g>L00=l07>LLi`0_7>L27oo0006Oom3Li`0 0g`0LiacW008Li`30003Li`2O00L00YcW0<0 00AcW003O01cW7>L00QcW003001cW7>L0:icW0Qoo`001Woo@G>L00=l07>LLi`037>L0`0017>L00=l 07>LLi`01W>L00<007>LLi`0[g>L27oo0006OomALi`30004Li`00g`0LiacW004Li`00`00LiacW02` Li`8Ool000Iooe9cW0<000AcW003O01cW7>L009cW003001cW7>L0;5cW0Qoo`001WooDg>L0`0017>L 00Al07>LLi`00;AcW0Qoo`001WooE7>L0`0017>L00=l0000Li`0]7>L27oo0006OomELi`30003Li`0 0`00O01cW02dLi`8Ool000IooeIcW0<00005Li`007>LLial002dLi`8Ool000IooeMcW0<000AcW003 O01cW7>L0;5cW0Qoo`001WooF7>L0`0017>L00=l07>LLi`0/7>L27oo0006OomGLi`00`00Li`00002 0004Li`00g`0LiacW02_Li`8Ool000IooeIcW004001cW7>LLi`30004Li`00g`0LiacW02^Li`8Ool0 00IooeEcW003001cW7>L00=cW0<000AcW003O01cW7>L0:ecW0Qoo`001WooE7>L00<007>LLi`01G>L 0`0017>L00=l07>LLi`0[7>L27oo0006OomCLi`00`00LiacW007Li`30004Li`00g`0LiacW02[Li`8 Ool000Iooe9cW003001cW7>L00UcW0<000AcW003O01cW7>L0:YcW0Qoo`001WooDG>L00<007>LLi`0 2g>L0`0017>L00=l07>LLi`0ZG>L27oo0006Oom@Li`00`00LiacW00=Li`30004Li`00g`0LiacW02X Li`8Ool000IoodmcW003001cW7>L00mcW0<000AcW003O01cW7>L04AcW080065cW0Qoo`001WooHW>L 1@000W>L00=l07>LLi`0@7>L1@00HG>L27oo0006OomSLi`300001G>L00000000O000?W>L0`000W>L 0P00HW>L27oo0006OomSLi`40003Li`00`00O01cW00ALi`00g`0LiacW00VLi`20004Li`00`00Li`0 001RLi`8Ool000Ioof=cW003001cW000008000AcW003O000000000icW003O01cW7>L02AcW0<000Ec W004001cW7>L001RLi`8Ool000IoofAcW003001cW000008000AcW003O01cW000008000YcW003O01c W7>L029cW0<000McW004001cW7>L001SLi`8Ool000IoofAcW003001cW7>L00<000AcW004O01cW7>L Li`30006Li`00g`0LiacW00PLi`30009Li`01@00LiacW7>L0000Hg>L27oo0006OomTLi`01000Liac W7>L0`0017>L00=l07>LLi`00g>L0P000g>L00=l07>LLi`07g>L0P002g>L00<007>LLi`00W>L00<0 07>LLi`0HG>L27oo0006OomULi`01000LiacW7>L0`0017>L00=l07>LLi`01W>L00=l07>LLi`0;7>L 00<007>LLi`00W>L00<007>LLi`0HW>L27oo0006OomULi`00`00LiacW002Li`30003Li`00g`0Liac W005Li`00g`0LiacW00/Li`00`00LiacW003Li`00`00LiacW01RLi`8Ool000IoofEcW003001cW7>L 00=cW0<000=cW003O01cW7>L00=cW003O01cW7>L02acW003001cW7>L00=cW003001cW7>L06=cW0Qo o`001WooIW>L00<007>LLi`00g>L0`000g>L00El07>LLiacW7`002icW003001cW7>L00AcW003001c W7>L06=cW0Qoo`001WooIW>L00<007>LLi`017>L0`000g>L00=l07>LO000;W>L00<007>LLi`01G>L 00<007>LLi`0Hg>L27oo0006OomWLi`00`00LiacW004Li`30002Li`2O00^Li`00`00LiacW005Li`0 0`00LiacW01TLi`8Ool000IoofMcW003001cW7>L00EcW0<00004O01cW7>LO00/Li`00`00LiacW006 Li`00`00LiacW01TLi`8Ool000IoofMcW003001cW7>L00IcW003001l000000=cW003O01cW7>L02Qc W003001cW7>L00McW003001cW7>L06AcW0Qoo`001WooJ7>L00<007>LLi`01G>L00Al0000000000=c W003O01cW7>L02IcW003001cW7>L00McW003001cW7>L06EcW0Qoo`001WooJ7>L00<007>LLi`017>L 00=l07>LLi`00`000g>L00=l07>LLi`097>L00<007>LLi`027>L00<007>LLi`0IG>L27oo0006OomX Li`00`00LiacW003Li`00g`0LiacW002Li`30003Li`00g`0LiacW00RLi`00`00LiacW009Li`00`00 LiacW01ULi`8Ool000IoofUcW005001cW7>LLial0006Li`30003Li`00g`0LiacW00PLi`00`00Liac W009Li`00`00LiacW01VLi`8Ool000IoofUcW004001cW7>LO008Li`30003Li`00g`0LiacW00NLi`0 0`00LiacW00:Li`00`00LiacW01VLi`8Ool000Ioof]cW003O01cW7>L00QcW0<000=cW003O01cW7>L 01acW003001cW7>L07AcW0Qoo`001WooJW>L00=l07>LLi`02W>L0`000g>L00=l07>LLi`06W>L00<0 07>LLi`0MG>L27oo0006OomhLi`30002Li`00g`0LiacW00ILi`00`00LiacW01fLi`8Ool000IoogUc W0<0009cW003O01cW7>L01McW003001cW7>L07McW0Qoo`001WooNW>L0`000W>L00=l07>LLi`05G>L 00<007>LLi`0N7>L27oo0006OomkLi`30002Li`00g`0LiacW00CLi`00`00LiacW01iLi`8Ool000Io ogacW0<00003Lial07>L01=cW003001cW7>L07YcW0Qoo`001WooOG>L0`0000=cW7`0Li`04G>L00<0 07>LLi`0Ng>L27oo0006OomnLi`300000g>LO01cW00?Li`00`00LiacW01lLi`8Ool000IoogmcW0<0 0003Lial07>L00ecW08007icW0Qoo`001WooP7>L0`0000=cW7`0Li`02g>L0P00Og>L27oo0006Oon1 Li`300000g>LO01cW009Li`20020Li`8Ool000Iooh9cW0<00003Lial07>L00McW080085cW0Qoo`00 1WooPg>L0`0000=l07>LLi`01G>L0P00PW>L27oo0006Oon4Li`300000g`0LiacW003Li`20023Li`8 Ool000IoohEcW0<00004O01cW7>LLi`20024Li`8Ool000IoohIcW0<00004O01cW0000025Li`8Ool0 00IoohMcW0<00003O00007>L08EcW0Qoo`001WooR7>L0`0000=l07>LLi`0Q7>L27oo0006Oon8Li`3 00000g>LO01cW024Li`8Ool000IoohMcW003001cW00000800003O01cW7>L08=cW0Qoo`001WooQW>L 00@007>LLiacW0<00003O01cW7>L089cW0Qoo`001WooQG>L00<007>LLi`00g>L0`0000=l07>LLi`0 PG>L27oo0006Oon4Li`00`00LiacW005Li`300000g`0LiacW020Li`8Ool000Iooh=cW003001cW7>L 00McW0800003O01cW7>L081cW0Qoo`001WooPW>L00<007>LLi`02G>L0P0000=l07>LLi`0Og>L27oo 0006Oon1Li`00`00LiacW00;Li`200000g`0LiacW01nLi`8Ool000Iooh1cW003001cW7>L00ecW080 0003O01cW7>L07ecW0Qoo`001WooOg>L00<007>LLi`03g>L0P0000=l07>LLi`0O7>L27oo0006OonB Li`00`00O000001mLi`8Ool000Iooi=cW003001l000007acW0Qoo`001WooU7>L00<007`00000Ng>L 27oo0006OonELi`00`00O000001jLi`8Ool000IooiIcW003001l000007UcW0Qoo`001WooUg>L00=l 00000000N7>L27oo0006OonHLi`00g`00000001gLi`8Ool000IooiUcW003O000000007IcW0Qoo`00 1WooVW>L00=l00000000MG>L27oo0006OonJLi`017`000000000M7>L27oo0006OonKLi`017`00000 00003G>L00=l07>LLi`0Hg>L27oo0006OonLLi`017`0000000002W>L0W`0IW>L27oo0006OonMLi`0 17`00000000027>L00=l07>LLi`0IW>L27oo0006OonMLi`00g`0Li`000020005Li`2O01YLi`8Ool0 00IooiicW003O01cW000008000=cW003O01cW7>L06UcW0Qoo`001WooWg>L00=l07>L00000P0000=c W7`0Li`0Jg>L27oo0006OonPLi`00g`0Li`00002O01]Li`8Ool000Iooj1cW003O01cW7`000<006ac W0Qoo`001WooX7>L0W`00W>L0`00Jg>L27oo0006OonOLi`017`0LiacW7`00W>L0`00JW>L27oo0006 OonMLi`2O003Li`017`0LiacW7>L0`00JG>L27oo0006OonLLi`00g`0LiacW004Li`017`0LiacW7>L 0`00J7>L27oo0006OonKLi`00g`0LiacW006Li`017`0LiacW7>L0`00Ig>L27oo0006OonILi`2O009 Li`00g`0LiacW002Li`3001VLi`8Ool000IooiQcW003O01cW7>L00YcW003O01cW7>L009cW0<006Ec W0Qoo`001WooUW>L0W`03W>L00=l07>LLi`00W>L0`00I7>L27oo0006OonELi`00g`0LiacW00?Li`0 0g`0LiacW002Li`3001SLi`8Ool000IoojMcW003O01cW7>L00=cW0<0069cW0Qoo`001WooZ7>L00=l 07>LLi`00g>L0`004W>L00<007>LLi`0C7>L27oo0006OonYLi`00g`0LiacW003Li`3000@Li`00`00 LiacW01=Li`8Ool000IoojUcW003O01cW7>L00AcW0<000icW003001cW7>L04icW0Qoo`001WooZW>L 00=l07>LLi`017>L0`0037>L00<007>LLi`0Cg>L27oo0006Oon[Li`00g`0LiacW004Li`3000:Li`0 0`00LiacW01@Li`8Ool000IoojacW003O01cW7>L00AcW0<000QcW003001cW7>L055cW0Qoo`001Woo [7>L00=l07>LLi`01G>L0`001W>L00<007>LLi`0DW>L27oo0006Oon]Li`00g`0LiacW005Li`30004 Li`00`00LiacW01CLi`8Ool000IoojicW003O01cW7>L00EcW0<0009cW003001cW7>L05AcW0Qoo`00 1Woo[g>L00=l07>LLi`01G>L1000Eg>L27oo0006Oon_Li`00g`0LiacW006Li`3001GLi`8Ool000Io ok1cW003O01cW7>L00IcW0<005IcW0Qoo`001Woo/G>L00=l07>LLi`017>L00<007>L00000P00EG>L 27oo0006OonaLi`00g`0LiacW003Li`01000LiacW7>L0`00E7>L27oo0006OonbLi`01G`0LiacW7>L 00001G>L0`00Dg>L27oo0006OoncLi`00g`0Li`00007Li`3001BLi`8Ool000Iook=cW003O00007>L 00QcW0<0055cW0Qoo`001Woo/g>L00<007`0Li`02G>L0`00D7>L27oo0006OonbLi`00`00Lial000; Li`3001?Li`8Ool000Iook5cW005001cW7>LLial000;Li`3001>Li`8Ool000Iook1cW003001cW7>L 00=cW003O01cW7>L00UcW0<004ecW0Qoo`001Woo]W>L00=l07>LLi`02W>L0`00C7>L27oo0006Oong Li`00g`0LiacW00:Li`3001;Li`8Ool000IookQcW003O01cW7>L00YcW0<004YcW0Qoo`001Woo^7>L 00=l07>LLi`02g>L0`001g>L00<007>LLi`05g>L00<007>LLi`09G>L27oo0006OoniLi`00g`0Liac W00;Li`30006Li`00`00LiacW00GLi`00`00LiacW00ULi`8Ool000IookYcW003O01cW7>L00]cW0<0 00EcW003001cW7>L01McW003001cW7>L02EcW0Qoo`001Woo^W>L00=l07>LLi`037>L0`0017>L00<0 07>LLi`05g>L00<007>LLi`09G>L27oo0006OonkLi`00g`0LiacW00L00acW0<0009cW003001cW7>L01McW003001c W7>L02EcW0Qoo`001Woo_7>L00=l07>LLi`03G>L0`0000=cW000Li`067>L00<007>LLi`09G>L27oo 0006OonmLi`00g`0LiacW00=Li`4000ILi`00`00LiacW00ULi`8Ool000IookicW003O01cW7>L00ec W0<001UcW003001cW7>L02EcW0Qoo`001Woo_W>L00=l07>LLi`03W>L0`0067>L00<007>LLi`09G>L 27oo0006OonoLi`00g`0LiacW00>Li`3000GLi`00`00LiacW00ULi`8Ool000Iool1cW003O01cW7>L 00ecW0@001IcW003001cW7>L02EcW0Qoo`001Woo`7>L00=l07>LLi`03G>L00<007>L00000P005G>L 00<007>LLi`09G>L27oo0006Ooo1Li`00g`0LiacW00L00]cW004001cW7>LLi`3000CLi`00`00LiacW00ULi`8Ool000Io ol9cW003O01cW7>L00]cW003001cW7>L009cW0<0019cW003001cW7>L02EcW0Qoo`001Woo`g>L00=l 07>LLi`02W>L00<007>LLi`00g>L0`004G>L00<007>LLi`09G>L27oo0006Ooo4Li`00g`0LiacW009 Li`00`00LiacW004Li`3000@Li`00`00LiacW00ULi`8Ool000IoolEcW003O01cW7>L00QcW003001c W7>L00EcW0<000mcW003001cW7>L02EcW0Qoo`001WooaG>L00=l07>LLi`027>L00<007>LLi`01W>L 0`003W>L00<007>LLi`09G>L27oo0006Ooo6Li`00g`0LiacW007Li`00`00LiacW007Li`3000=Li`0 0`00LiacW00ULi`8Ool000IoolMcW003O01cW7>L00IcW003001cW7>L00QcW0<000acW003001cW7>L 02EcW0Qoo`001Wooag>L00=l07>LLi`01W>L00<007>LLi`02G>L0`002g>L00<007>LLi`09G>L27oo 0006Ooo8Li`00g`0LiacW005Li`00`00LiacW00:Li`3000:Li`00`00LiacW00ULi`8Ool000IoolUc W003O01cW7>L00P000YcW0<000IcW0P002=cW0Qoo`001WoobG>L00=l0000000017>L00@007>LLiac W08000UcW0<000=cW08000=cW003001cW7>L009cW080025cW0Qoo`001WoobG>L00<007`0Li`017>L 00<007>LLi`00g>L0P0027>L0`0000=cW000Li`017>L00<007>LLi`017>L00<007>LLi`07W>L27oo 0006Ooo9Li`00`00Lial0004Li`00`00LiacW004Li`00`00LiacW007Li`30006Li`00`00LiacW005 Li`00`00LiacW00MLi`8Ool000IoolMcW080009cW003O01cW7>L009cW003001cW7>L00EcW003001c W7>L00McW0<000EcW003001cW7>L00IcW003001cW7>L01acW0Qoo`001WooaW>L00<007>LLi`00g>L 00El07>LLiacW00000QcW003001cW7>L00EcW003001cW000008000AcW003001cW7>L00IcW003001c W7>L01acW0Qoo`001WooaW>L00<007>LLi`017>L00Al07>LLi`000UcW003001cW7>L00AcW003001c W7>L00<000=cW003001cW7>L00McW003001cW7>L01]cW0Qoo`001WooaG>L00<007>LLi`01G>L00Al 07>LLi`000UcW003001cW7>L00=cW003001cW7>L009cW0<0009cW003001cW7>L00McW003001cW7>L 01]cW0Qoo`001WooaG>L00<007>LLi`01W>L00=l07>L00002W>L00<007>LLi`00W>L00<007>LLi`0 0g>L0`0000=cW000Li`02G>L00<007>LLi`06W>L27oo0006Ooo5Li`00`00LiacW007Li`00g`0001c W009Li`01@00LiacW7>L00001g>L10002W>L00<007>LLi`06W>L27oo0006Ooo5Li`00`00LiacW007 Li`00g`0001cW009Li`01@00LiacW7>L000027>L0`002W>L00<007>LLi`06W>L27oo0006OoniLia9 000@Li`8Ool000IoolEcW003001cW7>L00QcW003001cW7>L00QcW003001cW7>L009cW003001cW7>L 00McW003001cW7>L00QcW003001cW7>L01YcW0Qoo`001WooaG>L00<007>LLi`027>L00<007>LLi`0 27>L00<007>LLi`00W>L00<007>LLi`01g>L00<007>LLi`027>L00<007>LLi`06W>L27oo0006Ooo5 Li`00`00LiacW008Li`00`00LiacW007Li`00`00LiacW003Li`00`00LiacW007Li`00`00LiacW008 Li`00`00LiacW00JLi`8Ool000IoolIcW003001cW7>L00McW003001cW7>L00McW003001cW7>L00=c W003001cW7>L00McW003001cW7>L00QcW003001cW7>L01YcW0Qoo`001WooaW>L00<007>LLi`01g>L 00<007>LLi`01W>L00<007>LLi`017>L00<007>LLi`01g>L00<007>LLi`01g>L00<007>LLi`06g>L 27oo0006Ooo7Li`00`00LiacW006Li`00`00LiacW006Li`00`00LiacW005Li`00`00LiacW006Li`0 0`00LiacW007Li`00`00LiacW00KLi`8Ool000IoolQcW003001cW7>L00EcW003001cW7>L00EcW003 001cW7>L00McW003001cW7>L00EcW003001cW7>L00IcW003001cW7>L01acW0Qoo`001WoobG>L00<0 07>LLi`017>L00<007>LLi`01G>L00<007>LLi`027>L00<007>LLi`017>L00<007>LLi`01G>L00<0 07>LLi`07G>L27oo0006Ooo:Li`00`00LiacW003Li`00`00LiacW003Li`2000LLi`2000?Li`20003Li`0 1000LiacW7>L0P008W>L27oo0006Ooo=Li`7000CLi`7000TLi`8Ool000Ioom1cW003001cW7>L01Mc W003001cW7>L02EcW0Qoo`001Wood7>L00<007>LLi`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`0 0`00LiacW00GLi`00`00LiacW00ULi`8Ool000Ioom1cW003001cW7>L01McW003001cW7>L02EcW0Qo o`001Wood7>L00<007>LLi`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`00`00LiacW00GLi`00`00 LiacW00ULi`8Ool000Ioom1cW003001cW7>L01McW003001cW7>L02EcW0Qoo`001Wood7>L00<007>L Li`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`00`00LiacW00GLi`00`00LiacW00ULi`8Ool000Io om1cW003001cW7>L01McW003001cW7>L02EcW0Qoo`001Wood7>L00<007>LLi`05g>L00<007>LLi`0 9G>L27oo0006Ooo@Li`00`00LiacW00GLi`00`00LiacW00ULi`8Ool000Ioom1cW003001cW7>L01Mc W003001cW7>L02EcW0Qoo`001Wood7>L00<007>LLi`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`0 0`00LiacW00GLi`00`00LiacW00ULi`8Ool000Ioom1cW003001cW7>L01McW003001cW7>L02EcW0Qo o`001Wood7>L00<007>LLi`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`00`00LiacW00GLi`00`00 LiacW00ULi`8Ool000Ioom1cW003001cW7>L01McW003001cW7>L02EcW0Qoo`001Wood7>L00<007>L Li`05g>L00<007>LLi`09G>L27oo0006Ooo@Li`00`00LiacW00GLi`00`00LiacW00ULi`8Ool000Io om1cW003001cW7>L01McW003001cW7>L02EcW0Qoo`001Wood7>L00<007>LLi`05g>L00<007>LLi`0 9G>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8 Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`00 1Wooog>L4g>L27oo0006OoooLi`BLi`00`00Oomoo`06Ool000IooomcW19cW003001oogoo00Ioo`00 ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {287.813, 0}} -> {-0.874069, -0.856969, \ 0.00362728, 0.00362728}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[frameb, frame, pltO, pltOs, pltOax, pltOv, pltD, pltDs, pltDv, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic, PlotRange \[Rule] All];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.839656 0.960691 0.820415 0.960691 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .02381 m .02381 .97619 L .97619 .97619 L .97619 .02381 L F 0 g .008 w .02381 .02381 Mdot .97619 .97619 Mdot 2 Mabswid [ ] 0 setdash .83966 .82041 m .16034 .1411 L s .5 Mabswid .63586 .68455 m .70379 .61662 L s .46603 .51472 m .53397 .44679 L s .29621 .3449 m .36414 .27697 L s 0 0 0 r .5 .48076 m .36414 .3449 L s .43207 .36754 m .36414 .3449 L s .38678 .41283 m .36414 .3449 L s .5 .48076 m .63586 .3449 L s .61322 .41283 m .63586 .3449 L s .56793 .36754 m .63586 .3449 L s 0 g 2 Mabswid .09241 .20903 m .22828 .07317 L s .83966 .82041 m .93572 .91648 L .74359 .91648 L .83966 .82041 L s .93572 .9357 m .74359 .9357 L s 1 g .83966 .82041 m .83966 .82041 .03843 0 365.73 arc F 0 g newpath .83966 .82041 .03843 0 365.73 arc s 1 0 0 r .5 Mabswid .74728 .82041 m .7191 .77853 L .68912 .7339 L .66157 .6931 L .63551 .65498 L .60817 .6157 L .58217 .57921 L .55479 .54193 L .52863 .50752 L .50363 .47585 L .4772 .4437 L .4519 .41426 L .42773 .38735 L .40219 .36016 L .37784 .3354 L .35225 .31051 L .32797 .28787 L .30504 .26725 L .28118 .24645 L .25887 .22743 L .23599 .20817 L .2149 .19037 L .19567 .1738 L .17651 .15661 L .16034 .1411 L s .54201 .60694 m .62206 .55113 L s .39214 .41966 m .46276 .35442 L s .24931 .28248 m .31339 .2107 L s 0 g 2 Mabswid .09241 .20903 m .22828 .07317 L s .74728 .82041 m .84335 .91648 L .65121 .91648 L .74728 .82041 L s .84335 .9357 m .65121 .9357 L s 1 g .74728 .82041 m .74728 .82041 .03843 0 365.73 arc F 0 g newpath .74728 .82041 .03843 0 365.73 arc s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 288}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL0?mcW11cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000Iooomc W1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L 27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool0 00Iooc]cW003001cW7>L0=AcW0Qoo`001Woo>W>L0`00eG>L27oo0006OoliLi`3003FLi`8Ool000Io ocQcW0<00=McW0Qoo`001Woo=g>L0`00f7>L27oo0006OolfLi`3003ILi`8Ool000IoocEcW0<00=Yc W0Qoo`001Woo=7>L0`00fg>L27oo0006OolcLi`3003LLi`8Ool000Iooc9cW0<00=ecW0Qoo`001Woo L0`00gW>L27oo0006Ool`Li`3003OLi`8Ool000IoobmcW0<00>1cW0Qoo`001Woo;W>L0`00hG>L 27oo0006Ool]Li`3003RLi`8Ool000IoobacW0<00>=cW0Qoo`001Woo:g>L0`00i7>L27oo0006OolZ Li`3003ULi`8Ool000IoobUcW0<00>IcW0Qoo`001Woo:7>L0`00ig>L27oo0006OolWLi`3003XLi`8 Ool000IoobIcW0@00>QcW0Qoo`001Woo9G>L100000=l0000Li`0iW>L27oo0006OolTLi`30002Li`0 0`00O000003VLi`8Ool000Ioob=cW0<000AcW003001l00000>EcW0Qoo`001Woo8W>L0`001W>L00<0 07`00000i7>L27oo0006OolQLi`30008Li`00`00O000003SLi`8Ool000Ioob1cW0<000YcW003001l 00000>9cW0Qoo`001Woo7g>L0`0037>L00<007`0O000hG>L27oo0006OolNLi`3000>Li`200000g`0 LiacW03NLi`8Ool000IooaecW0<0011cW0800003O01cW7>L0=ecW0Qoo`001Woo77>L0`004W>L0P00 00=l07>LLi`0g7>L27oo0006OolKLi`3000DLi`200000g`0LiacW03KLi`8Ool000IooaYcW0<001Ic W0800003O01cW7>L0=YcW0Qoo`001Woo6G>L0`0067>L0P0000=l07>LLi`0fG>L27oo0006OolHLi`3 000JLi`200000g`0LiacW03HLi`8Ool000IooaMcW0<001acW0800003O01cW7>L0=McW0Qoo`001Woo 5W>L0`007W>L0P0000=l07>LLi`0eW>L27oo0006OolELi`3000PLi`20002O03FLi`8Ool000IooaAc W0<0029cW0<00003O01cW7>L0==cW0Qoo`001Woo4g>L0`0097>L0`0000=l07>LLi`0dW>L27oo0006 OolDLi`00`00LiacW00TLi`300000g`0LiacW00BLi`00g`0LiacW02lLi`8Ool000IoocacW0<00003 O01cW7>L011cW003O01cW7>L0;ecW0Qoo`001Woo?G>L0`000W`03g>L00=l07>LLi`0_W>L27oo0006 OolnLi`300000g>LO01cW00L00]cW003 O01cW7>L0;mcW0Qoo`001Woo@7>L0`0000=cW7`0Li`02G>L00=l07>LLi`0`7>L27oo0006Oom1Li`3 00000g>LO01cW007Li`00g`0LiacW031Li`8Ool000Iood9cW0<00003Lial07>L00EcW003O01cW7>L 0<9cW0Qoo`001Woo@g>L0`0000=cW7`0O0000g>L00=l07>LLi`0`g>L27oo0006Oom4Li`30002Li`0 0g`0Lial0036Li`8Ool000IoodEcW0<0009cW003O01cW7>L0L0`0000=cW7`0 O000aW>L27oo0006Oom7Li`2000017`0LiacW7`0aG>L27oo0006Oom8Li`00g`000000002Li`2O033 Li`8Ool000IoodMcW003O01cW000008000=cW003O01cW7>L0<1cW0Qoo`001WooAW>L00Al07>LLiac W0<000=cW003O01cW7>L0;mcW0Qoo`001WooAG>L00=l07>LLi`00g>L0`000g>L00=l07>LLi`0_W>L 27oo0006Oom4Li`00g`0LiacW005Li`30003Li`00g`0LiacW02mLi`8Ool000IoodAcW003O01cW7>L 00IcW0<000=cW003O01cW7>L0;acW0Qoo`001Woo@g>L00=l07>LLi`027>L0`000g>L0W`037>L00<0 07>LLi`0[G>L27oo0006Oom2Li`00g`0LiacW00:Li`30004Li`00g`0LiacW008Li`00`00LiacW02^ Li`8Ool000Iood5cW003O01cW7>L00acW0<000AcW003O01cW7>L00IcW003001cW7>L0:mcW0Qoo`00 1WooDG>L0`0017>L00=l07>LLi`017>L00<007>LLi`0/7>L27oo0006OomBLi`30004Li`00g`0Liac W002Li`00`00LiacW02aLi`8Ool000Iooe=cW0<000AcW004O01cW7>L002dLi`8Ool000IooeAcW0<0 00AcW003O00007>L0;AcW0Qoo`001WooEG>L0`000g>L00<007`0Li`0]7>L27oo0006OomFLi`30000 1G>L001cW7>LO000]7>L27oo0006OomGLi`30004Li`00g`0LiacW02aLi`8Ool000IooeQcW0<000Ac W003O01cW7>L0;1cW0Qoo`001WooEg>L00<007>L00000P0017>L00=l07>LLi`0[g>L27oo0006OomF Li`01000LiacW7>L0`0017>L00=l07>LLi`0[W>L27oo0006OomELi`00`00LiacW003Li`30004Li`0 0g`0LiacW02]Li`8Ool000IooeAcW003001cW7>L00EcW0<000AcW003O01cW7>L0:acW0Qoo`001Woo Dg>L00<007>LLi`01g>L0`0017>L00=l07>LLi`0Zg>L27oo0006OomBLi`00`00LiacW009Li`30004 Li`00g`0LiacW02ZLi`8Ool000Iooe5cW003001cW7>L00]cW0<000AcW003O01cW7>L0:UcW0Qoo`00 1WooD7>L00<007>LLi`03G>L0`0017>L00=l07>LLi`0Z7>L27oo0006Oom?Li`00`00LiacW00?Li`3 0004Li`00g`0LiacW014Li`2001QLi`8Ool000Ioof9cW0D0009cW003O01cW7>L041cW0D0065cW0Qo o`001WooHg>L0`0000EcW000000007`003icW0<0009cW080069cW0Qoo`001WooHg>L10000g>L00<0 07`0Li`04G>L00=l07>LLi`09W>L0P0017>L00<007>L0000HW>L27oo0006OomSLi`00`00Li`00002 0004Li`00g`00000000>Li`00g`0LiacW00TLi`30005Li`01000LiacW000HW>L27oo0006OomTLi`0 0`00Li`000020004Li`00g`0Li`00002000:Li`00g`0LiacW00RLi`30007Li`01000LiacW000Hg>L 27oo0006OomTLi`00`00LiacW0030004Li`017`0LiacW7>L0`001W>L00=l07>LLi`087>L0`002G>L 00D007>LLiacW00006=cW0Qoo`001WooI7>L00@007>LLiacW0<000AcW003O01cW7>L00=cW08000=c W003O01cW7>L01mcW08000]cW003001cW7>L009cW003001cW7>L065cW0Qoo`001WooIG>L00@007>L LiacW0<000AcW003O01cW7>L00IcW003O01cW7>L02acW003001cW7>L009cW003001cW7>L069cW0Qo o`001WooIG>L00<007>LLi`00W>L0`000g>L00=l07>LLi`01G>L00=l07>LLi`0;7>L00<007>LLi`0 0g>L00<007>LLi`0HW>L27oo0006OomULi`00`00LiacW003Li`30003Li`00g`0LiacW003Li`00g`0 LiacW00/Li`00`00LiacW003Li`00`00LiacW01SLi`8Ool000IoofIcW003001cW7>L00=cW0<000=c W005O01cW7>LLial000^Li`00`00LiacW004Li`00`00LiacW01SLi`8Ool000IoofIcW003001cW7>L 00AcW0<000=cW003O01cW7`002icW003001cW7>L00EcW003001cW7>L06=cW0Qoo`001WooIg>L00<0 07>LLi`017>L0`000W>L0W`0;W>L00<007>LLi`01G>L00<007>LLi`0I7>L27oo0006OomWLi`00`00 LiacW005Li`3000017`0LiacW7`0;7>L00<007>LLi`01W>L00<007>LLi`0I7>L27oo0006OomWLi`0 0`00LiacW006Li`00`00O0000003Li`00g`0LiacW00XLi`00`00LiacW007Li`00`00LiacW01TLi`8 Ool000IoofQcW003001cW7>L00EcW004O00000000003Li`00g`0LiacW00VLi`00`00LiacW007Li`0 0`00LiacW01ULi`8Ool000IoofQcW003001cW7>L00AcW003O01cW7>L00<000=cW003O01cW7>L02Ac W003001cW7>L00QcW003001cW7>L06EcW0Qoo`001WooJ7>L00<007>LLi`00g>L00=l07>LLi`00W>L 0`000g>L00=l07>LLi`08W>L00<007>LLi`02G>L00<007>LLi`0IG>L27oo0006OomYLi`01@00Liac W7>LO0001W>L0`000g>L00=l07>LLi`087>L00<007>LLi`02G>L00<007>LLi`0IW>L27oo0006OomY Li`01000LiacW7`027>L0`000g>L00=l07>LLi`07W>L00<007>LLi`02W>L00<007>LLi`0IW>L27oo 0006Oom[Li`00g`0LiacW008Li`30003Li`00g`0LiacW00LLi`00`00LiacW01dLi`8Ool000IoofYc W003O01cW7>L00YcW0<000=cW003O01cW7>L01YcW003001cW7>L07EcW0Qoo`001WooN7>L0`000W>L 00=l07>LLi`06G>L00<007>LLi`0MW>L27oo0006OomiLi`30002Li`00g`0LiacW00GLi`00`00Liac W01gLi`8Ool000IoogYcW0<0009cW003O01cW7>L01EcW003001cW7>L07QcW0Qoo`001WooNg>L0`00 0W>L00=l07>LLi`04g>L00<007>LLi`0NG>L27oo0006OomlLi`300000g>LO01cW00CLi`00`00Liac W01jLi`8Ool000IoogecW0<00003Lial07>L015cW003001cW7>L07]cW0Qoo`001WooOW>L0`0000=c W7`0Li`03g>L00<007>LLi`0O7>L27oo0006OomoLi`300000g>LO01cW00=Li`2001nLi`8Ool000Io oh1cW0<00003Lial07>L00]cW08007mcW0Qoo`001WooPG>L0`0000=cW7`0Li`02G>L0P00P7>L27oo 0006Oon2Li`300000g>LO01cW007Li`20021Li`8Ool000Iooh=cW0<00003O01cW7>L00EcW080089c W0Qoo`001WooQ7>L0`0000=l07>LLi`00g>L0P00Pg>L27oo0006Oon5Li`3000017`0LiacW7>L0P00 Q7>L27oo0006Oon6Li`3000017`0Li`00000QG>L27oo0006Oon7Li`300000g`0001cW025Li`8Ool0 00IoohQcW0<00003O01cW7>L08AcW0Qoo`001WooR7>L0`0000=cW7`0Li`0Q7>L27oo0006Oon7Li`0 0`00Li`0000200000g`0LiacW023Li`8Ool000IoohIcW004001cW7>LLi`300000g`0LiacW022Li`8 Ool000IoohEcW003001cW7>L00=cW0<00003O01cW7>L085cW0Qoo`001WooQ7>L00<007>LLi`01G>L 0`0000=l07>LLi`0P7>L27oo0006Oon3Li`00`00LiacW007Li`200000g`0LiacW020Li`8Ool000Io oh9cW003001cW7>L00UcW0800003O01cW7>L07mcW0Qoo`001WooPG>L00<007>LLi`02g>L0P0000=l 07>LLi`0OW>L27oo0006Oon0Li`00`00LiacW00=Li`200000g`0LiacW01mLi`8Ool000IoogmcW003 001cW7>L00mcW0800003O01cW7>L07acW0Qoo`001WooTW>L00<007`00000OG>L27oo0006OonCLi`0 0`00O000001lLi`8Ool000IooiAcW003001l000007]cW0Qoo`001WooUG>L00<007`00000NW>L27oo 0006OonFLi`00`00O000001iLi`8Ool000IooiMcW003O000000007QcW0Qoo`001WooV7>L00=l0000 0000Mg>L27oo0006OonILi`00g`00000001fLi`8Ool000IooiYcW003O000000007EcW0Qoo`001Woo VW>L00Al0000000007AcW0Qoo`001WooVg>L00Al0000000000ecW003O01cW7>L06=cW0Qoo`001Woo W7>L00Al0000000000YcW09l06IcW0Qoo`001WooWG>L00Al0000000000QcW003O01cW7>L06IcW0Qo o`001WooWG>L00=l07>L00000P001G>L0W`0JG>L27oo0006OonNLi`00g`0Li`000020003Li`00g`0 LiacW01YLi`8Ool000IooimcW003O01cW00000800003Lial07>L06]cW0Qoo`001WooX7>L00=l07>L 00000W`0KG>L27oo0006OonPLi`00g`0Lial0003001/Li`8Ool000Iooj1cW09l009cW0<006]cW0Qo o`001WooWg>L00Al07>LLial009cW0<006YcW0Qoo`001WooWG>L0W`00g>L00Al07>LLiacW0<006Uc W0Qoo`001WooW7>L00=l07>LLi`017>L00Al07>LLiacW0<006QcW0Qoo`001WooVg>L00=l07>LLi`0 1W>L00Al07>LLiacW0<006McW0Qoo`001WooVG>L0W`02G>L00=l07>LLi`00W>L0`00IW>L27oo0006 OonHLi`00g`0LiacW00:Li`00g`0LiacW002Li`3001ULi`8Ool000IooiIcW09l00icW003O01cW7>L 009cW0<006AcW0Qoo`001WooUG>L00=l07>LLi`03g>L00=l07>LLi`00W>L0`00Hg>L27oo0006OonW Li`00g`0LiacW003Li`3001RLi`8Ool000IoojQcW003O01cW7>L00=cW0<0019cW003001cW7>L04ac W0Qoo`001WooZG>L00=l07>LLi`00g>L0`0047>L00<007>LLi`0CG>L27oo0006OonYLi`00g`0Liac W004Li`3000>Li`00`00LiacW01>Li`8Ool000IoojYcW003O01cW7>L00AcW0<000acW003001cW7>L 04mcW0Qoo`001WooZg>L00=l07>LLi`017>L0`002W>L00<007>LLi`0D7>L27oo0006Oon/Li`00g`0 LiacW004Li`30008Li`00`00LiacW01ALi`8Ool000IoojacW003O01cW7>L00EcW0<000IcW003001c W7>L059cW0Qoo`001Woo[G>L00=l07>LLi`01G>L0`0017>L00<007>LLi`0Dg>L27oo0006Oon^Li`0 0g`0LiacW005Li`30002Li`00`00LiacW01DLi`8Ool000IoojmcW003O01cW7>L00EcW0@005McW0Qo o`001Woo[g>L00=l07>LLi`01W>L0`00Eg>L27oo0006Oon`Li`00g`0LiacW006Li`3001FLi`8Ool0 00Iook5cW003O01cW7>L00AcW003001cW000008005EcW0Qoo`001Woo/G>L00=l07>LLi`00g>L00@0 07>LLiacW0<005AcW0Qoo`001Woo/W>L00El07>LLiacW00000EcW0<005=cW0Qoo`001Woo/g>L00=l 07>L00001g>L0`00DW>L27oo0006OoncLi`00g`0001cW008Li`3001ALi`8Ool000Iook=cW003001l 07>L00UcW0<0051cW0Qoo`001Woo/W>L00<007>LO0002g>L0`00Cg>L27oo0006OonaLi`01@00Liac W7>LO0002g>L0`00CW>L27oo0006Oon`Li`00`00LiacW003Li`00g`0LiacW009Li`3001=Li`8Ool0 00IookIcW003O01cW7>L00YcW0<004acW0Qoo`001Woo]g>L00=l07>LLi`02W>L0`00Bg>L27oo0006 OonhLi`00g`0LiacW00:Li`3001:Li`8Ool000IookQcW003O01cW7>L00]cW0<004UcW0Qoo`001Woo ^G>L00=l07>LLi`02g>L0`00B7>L27oo0006OonjLi`00g`0LiacW00;Li`30017Li`8Ool000IookYc W003O01cW7>L00acW0<004IcW0Qoo`001Woo^g>L00=l07>LLi`037>L0`00AG>L27oo0006OonlLi`0 0g`0LiacW00L00ecW0<004=cW0Qoo`001Woo_G>L00=l 07>LLi`03G>L0`00@W>L27oo0006OonnLi`00g`0LiacW00=Li`30011Li`8Ool000IookicW003O01c W7>L00icW0<0041cW0Qoo`001Woo_g>L00=l07>LLi`03W>L0`00?g>L27oo0006Ooo0Li`00g`0Liac W00>Li`3000nLi`8Ool000Iool1cW003O01cW7>L00mcW0<003ecW0Qoo`001Woo`G>L00=l07>LLi`0 3g>L0`00?7>L27oo0006Ooo2Li`00g`0LiacW00?Li`3000kLi`8Ool000Iool9cW003O01cW7>L011c W0<003YcW0Qoo`001Woo`g>L00=l07>LLi`047>L0`00>G>L27oo0006Ooo4Li`00g`0LiacW00@Li`3 000hLi`8Ool000IoolEcW003O01cW7>L011cW0<003McW0Qoo`001WooaG>L00=l07>LLi`04G>L0`00 =W>L27oo0006Ooo6Li`00g`0LiacW00ALi`3000eLi`8Ool000IoolMcW003O01cW7>L015cW0<003Ac W0Qoo`001Wooag>L00=l07>LLi`04W>L0`00L27oo0006Ooo8Li`00g`0LiacW00BLi`3000bLi`8 Ool000IoolUcW003O000000000X000QcW0<000AcW0`0025cW0Qoo`001WoobG>L00=l000000003000 1g>L0`000W>L3P0087>L27oo0006Ooo9Li`2000:Ool30008Li`6000:Ool3000OLi`8Ool000IoolMc W0<000eoo`8000QcW0@000aoo`<001icW0Qoo`001Wooag>L0`003Woo0P0027>L0P003Woo0P007W>L 27oo0006Ooo6Li`2000@Ool30006Li`2000@Ool2000MLi`8Ool000IoolIcW003001oogoo011oo`80 00IcW003001oogoo011oo`03001cW7>L01]cW0Qoo`001WooaG>L0P004goo0P0017>L0P004Woo0P00 77>L27oo0006Ooo5Li`00`00Oomoo`0COol00`00LiacW002Li`00`00Oomoo`0BOol00`00LiacW00J Li`8Ool000IoolAcW08001Aoo`8000=cW08001=oo`8001acW0Qoo`001Wooa7>L0P0057oo0P000W>L 0`004goo0`006g>L27oo0006Ooo4Li`2000DOol20003Li`2000COol3000KLi`8Ool000IoolAcW080 01Aoo`8000=cW08001=oo`<001]cW0Qoo`001WooaG>L00<007ooOol04Woo0P000g>L0P004goo0P00 77>L27oo0006Ooo5Li`2000COol20003Li`2000COol2000LLi`8Ool000IoolIcW003001oogoo015o o`03001cW7>L00=cW003001oogoo015oo`8001acW0Qoo`001WooaW>L0P004Goo0P001G>L0P004Woo 0P0077>L27oo0006Ooo7Li`2000@Ool00`00LiacW005Li`2000@Ool2000MLi`8Ool000IoolMcW0<0 00ioo`8000McW0<000ioo`<001ecW0Qoo`001Wooag>L10002goo10001g>L10002goo10007W>L27oo 0006Ooo6Li`60008Ool70005Li`70008Ool6000MLi`8Ool000IoolEcW0<0009cW0D000=oo`D0009c W0<000=cW0<0009cW0D000=oo`D0009cW0<001acW0Qoo`001Wooa7>L0`0017>L2P001G>L0`0000Ac W000000000EcW0X000AcW0<001]cW0Qoo`001Woo`g>L0`0027>L1@0027>L1@0027>L1@0027>L0`00 6W>L27oo0006Ooo2Li`3000GLi`3000GLi`3000ILi`8Ool000Iool5cW0<001QcW0@001McW0<001Qc W0Qoo`001Woo`7>L0`0067>L0P0000AcW000000001McW0<001McW0Qoo`001Woo_g>L0`0067>L0`00 0W>L0`005g>L0`005W>L27oo0006OonnLi`3000HLi`30004Li`3000GLi`3000ELi`8Ool000Iookec W0<001QcW0<000IcW0<001McW0<001AcW0Qoo`001Woo_7>L0`0067>L0`0027>L0`005g>L0`004g>L 27oo0006OonkLi`3000HLi`3000:Li`3000GLi`3000BLi`8Ool000IookYcW0<001QcW0<000acW0<0 01McW0<0015cW0Qoo`001Woo^G>L0`0067>L0`003W>L0`005g>L0`0047>L27oo0006OonhLi`3000H Li`3000@Li`3000GLi`3000?Li`8Ool000IookMcW0<001QcW0<0019cW0<001McW0<000icW0Qoo`00 1Woo]W>L0`0067>L0`0057>L0`005g>L0`003G>L27oo0006OoneLi`3000HLi`3000FLi`3000GLi`3 000LE@002W>L27oo 0006OonbLiaG0009Li`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool0 00Iook=cW5@000]cW0Qoo`001Woo/g>LE0002g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qo o`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006 OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`BLi`00`00Oomoo`06 Ool000IooomcW19cW003001oogoo00Ioo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo003o OolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.874018, -0.853989, \ 0.00362693, 0.00362693}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Diagrammi tecnici (N, Q, M) [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]" }], "Section", Evaluatable->False], Cell[CellGroupData[{ Cell["Definizioni ", "Subsection"], Cell["\<\ Si vedano anche le definizioni gi\[AGrave] date per realizzare il disegno \ della configurazione originaria\ \>", "SmallText"], Cell[BoxData[ \(\(diaN[i_]\)[\[Zeta]_] := \(asseO[i]\)[\[Zeta]] + scN\ \(\(sNQM[ i]\)[\[Zeta]]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\ \ a\_2[i]\)], "Input"], Cell["Valori al bordo", "SmallText"], Cell[BoxData[ \(diaNb[ i_] := {\(asseO[i]\)[0] + scN\ \(\(sNQM[i]\)[ 0]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\ a\_2[ i]\ \[Xi], \(asseO[i]\)[L[i]] + scN\ \(\(sNQM[i]\)[ L[i]]\)\[LeftDoubleBracket]1\[RightDoubleBracket]\ a\_2[ i]\ \[Xi]}\)], "Input"], Cell["Segni dei valori al bordo", "SmallText"], Cell[BoxData[ \(diaNs[i_] := Block[{y1 = scN\ \(\(sNQM[i]\)[ 0]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ /. \[InvisibleSpace]datinum, y2 = scN\ \(\(sNQM[i]\)[ L[i]]\)\[LeftDoubleBracket]1\[RightDoubleBracket] \ /. \[InvisibleSpace]datinum, pt1 = \(asseO[i]\)[0] + 0.5\ y1\ a\_2[i] + 0.04\ a\_1[i], pt2 = \(asseO[i]\)[L[i]] + 0.5\ y2\ a\_2[i] - 0.04\ a\_1[i], dsh = 0.04}, Complement[{If[y1 \[NotEqual] 0, pt1 + dsh\ a\_1[i]\ \((\[Xi] - 0.5)\)], If[y1 > 0, pt1 + dsh\ a\_2[i]\ \((\[Xi] - 0.5)\)], If[y2 \[NotEqual] 0, pt2 + dsh\ a\_1[i]\ \((\[Xi] - 0.5)\)], If[y2 > 0, pt2 + dsh\ a\_2[ i]\ \((\[Xi] - 0.5)\)]}, {Null}]] /. \[InvisibleSpace]datinum\)], \ "Input"], Cell[BoxData[ \(\(figN := Table[\(diaN[i]\)[L[i] \[Xi]], {i, 1, travi}] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(figNb := Flatten[Table[diaNb[i], {i, 1, travi}], 1] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(figNs := Flatten[Table[diaNs[i], {i, 1, travi}], 1] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(pltN := ParametricPlot[Evaluate[Join[figN, figNb, figNs]], {\[Xi], 0, 1}, Axes \[Rule] False, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotStyle \[Rule] {{Hue[0.4]}}];\)\)], "Input"], Cell[BoxData[ \(\(diaQ[i_]\)[\[Zeta]_] := \(asseO[i]\)[\[Zeta]] - scQ\ \(\(sNQM[ i]\)[\[Zeta]]\)\[LeftDoubleBracket]2\[RightDoubleBracket]\ \ a\_2[i]\)], "Input"], Cell[BoxData[ \(diaQb[ i_] := {\(asseO[i]\)[0] - scQ\ \(\(sNQM[i]\)[ 0]\)\[LeftDoubleBracket]2\[RightDoubleBracket]\ a\_2[ i]\ \[Xi], \(asseO[i]\)[L[i]] - scQ\ \(\(sNQM[i]\)[ L[i]]\)\[LeftDoubleBracket]2\[RightDoubleBracket]\ a\_2[ i]\ \[Xi]}\)], "Input"], Cell[BoxData[ \(diaQs[i_] := Block[{y1 = scQ\ \(\(sNQM[i]\)[ 0]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ /. \[InvisibleSpace]datinum, y2 = scQ\ \(\(sNQM[i]\)[ L[i]]\)\[LeftDoubleBracket]2\[RightDoubleBracket] \ /. \[InvisibleSpace]datinum, pt1 = \(asseO[i]\)[0] - 0.5\ y1\ a\_2[i] + 0.04\ a\_1[i], pt2 = \(asseO[i]\)[L[i]] - 0.5\ y2\ a\_2[i] - 0.04\ a\_1[i], dsh = 0.04}, Complement[{If[y1 \[NotEqual] 0, pt1 + dsh\ a\_1[i]\ \((\[Xi] - 0.5)\)], If[y1 > 0, pt1 + dsh\ a\_2[i]\ \((\[Xi] - 0.5)\)], If[y2 \[NotEqual] 0, pt2 + dsh\ a\_1[i]\ \((\[Xi] - 0.5)\)], If[y2 > 0, pt2 + dsh\ a\_2[ i]\ \((\[Xi] - 0.5)\)]}, {Null}]] /. \[InvisibleSpace]datinum\)], \ "Input"], Cell[BoxData[ \(\(figQ := Table[\(diaQ[i]\)[L[i] \[Xi]], {i, 1, travi}] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(figQb := Flatten[Table[diaQb[i], {i, 1, travi}], 1] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(figQs := Flatten[Table[diaQs[i], {i, 1, travi}], 1] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(pltQ := ParametricPlot[Evaluate[Join[figQ, figQb, figQs]], {\[Xi], 0, 1}, Axes \[Rule] False, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotStyle \[Rule] {{Hue[0.6]}}];\)\)], "Input"], Cell[BoxData[ \(\(diaM[i_]\)[\[Zeta]_] := \(asseO[i]\)[\[Zeta]] - scM\ \(\(sNQM[ i]\)[\[Zeta]]\)\[LeftDoubleBracket]3\[RightDoubleBracket]\ \ a\_2[i]\)], "Input"], Cell[BoxData[ \(diaMb[ i_] := {\(asseO[i]\)[0] - scM\ \(\(sNQM[i]\)[ 0]\)\[LeftDoubleBracket]3\[RightDoubleBracket]\ a\_2[ i]\ \[Xi], \(asseO[i]\)[L[i]] - scM\ \(\(sNQM[i]\)[ L[i]]\)\[LeftDoubleBracket]3\[RightDoubleBracket]\ a\_2[ i]\ \[Xi]}\)], "Input"], Cell[BoxData[ \(\(figM := Table[\(diaM[i]\)[L[i] \[Xi]], {i, 1, travi}] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(figMb := Flatten[Table[diaMb[i], {i, 1, travi}], 1] /. datinum;\)\)], "Input"], Cell[BoxData[ \(\(pltM := ParametricPlot[Evaluate[Join[figM, figMb]], {\[Xi], 0, 1}, Axes \[Rule] False, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotStyle \[Rule] {{Hue[0.8]}}];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Fattori di scala [", StyleBox["\[FilledCircle]", FontColor->RGBColor[0, 0, 1]], "]" }], "Subsection"], Cell[BoxData[ \(\(scN := scQ;\)\)], "Input"], Cell[BoxData[ \(\(scQ = 0.004;\)\)], "Input"], Cell[BoxData[ \(\(scM = 0.03;\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Diagramma della forza normale", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[frameb, pltO, pltN, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic, PlotRange \[Rule] All];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.839656 0.960691 0.820415 0.960691 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .02381 m .02381 .97619 L .97619 .97619 L .97619 .02381 L F 0 g 2 Mabswid [ ] 0 setdash .83966 .82041 m .16034 .1411 L s 0 1 .4 r .5 Mabswid .91725 .74282 m .8819 .72306 L .84334 .7015 L .80713 .68126 L .77231 .66179 L .73525 .64107 L .69957 .62113 L .66164 .59993 L .62511 .5795 L .58996 .55985 L .55256 .53895 L .51656 .51882 L .48194 .49946 L .44507 .47885 L .40959 .45902 L .37187 .43793 L .33554 .41762 L .30059 .39809 L .2634 .37729 L .2276 .35728 L .18955 .33601 L .15289 .31551 L .11761 .29579 L .08009 .27482 L .0458 .25565 L s .83966 .82041 m .8428 .81727 L .84624 .81383 L .84946 .81061 L .85256 .80751 L .85586 .80421 L .85904 .80103 L .86242 .79766 L .86567 .7944 L .8688 .79127 L .87213 .78794 L .87533 .78474 L .87842 .78165 L .8817 .77837 L .88486 .77521 L .88822 .77185 L .89145 .76862 L .89456 .76551 L .89787 .7622 L .90106 .75901 L .90445 .75562 L .90772 .75236 L .91086 .74921 L .9142 .74587 L .91725 .74282 L s .16034 .1411 m .1557 .14575 L .15063 .15082 L .14587 .15558 L .14129 .16015 L .13642 .16503 L .13173 .16972 L .12675 .1747 L .12194 .1795 L .11732 .18412 L .11241 .18904 L .10768 .19377 L .10313 .19832 L .09828 .20317 L .09362 .20783 L .08866 .21279 L .08388 .21756 L .07929 .22216 L .0744 .22705 L .0697 .23175 L .06469 .23675 L .05988 .24157 L .05524 .24621 L .05031 .25114 L .0458 .25565 L s .14383 .23913 m .14273 .23803 L .14153 .23683 L .1404 .2357 L .13931 .23461 L .13816 .23346 L .13704 .23235 L .13586 .23116 L .13472 .23002 L .13363 .22893 L .13246 .22776 L .13134 .22664 L .13026 .22556 L .12911 .22441 L .128 .2233 L .12683 .22213 L .12569 .221 L .1246 .21991 L .12344 .21875 L .12233 .21763 L .12114 .21644 L .12 .2153 L .1189 .2142 L .11773 .21303 L .11666 .21196 L s .86487 .76803 m .86376 .76693 L .86256 .76573 L .86143 .7646 L .86035 .76351 L .85919 .76236 L .85808 .76124 L .8569 .76006 L .85576 .75892 L .85466 .75783 L .8535 .75666 L .85237 .75554 L .85129 .75446 L .85014 .75331 L .84904 .7522 L .84786 .75103 L .84673 .74989 L .84564 .7488 L .84448 .74764 L .84336 .74653 L .84218 .74534 L .84103 .7442 L .83993 .7431 L .83876 .74193 L .83769 .74086 L s .83769 .76803 m .8388 .76693 L .84 .76573 L .84113 .7646 L .84221 .76351 L .84337 .76236 L .84448 .76124 L .84566 .76006 L .8468 .75892 L .8479 .75783 L .84907 .75666 L .85019 .75554 L .85127 .75446 L .85242 .75331 L .85352 .7522 L .8547 .75103 L .85583 .74989 L .85692 .7488 L .85808 .74764 L .8592 .74653 L .86038 .74534 L .86153 .7442 L .86263 .7431 L .8638 .74193 L .86487 .74086 L s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 288}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo 0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000Io oomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L 4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8 Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`00 1Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006Oooo Li`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=c W0Qoo`001Wooog>L4g>L27oo0006OolXLi`00`00LiacW03WLi`8Ool000IoobMcW0030003k0000>Qc W0Qoo`001Woo9W>L0P?/0`00ig>L27oo0006OolULi`010?/LiacW7>L0`00iW>L27oo0006OolULi`0 0`?/LiacW002Li`3003ULi`8Ool000Ioob=cW083k0IcW0<00>AcW0Qoo`001Woo8W>L00<3k7>LLi`0 1g>L0`00hg>L27oo0006OolQLi`00`?/LiacW009Li`3003RLi`8Ool000Ioob5cW0030nacW7>L00Yc W0<00>5cW0Qoo`001Woo7g>L0P?/3W>L0`00h7>L27oo0006OolNLi`00`?/LiacW00?Li`3003OLi`8 Ool000IooaicW0030nacW7>L011cW0<00=icW0Qoo`001Woo77>L0P?/57>L0`00gG>L27oo0006OolK Li`00`?/LiacW00ELi`3003LLi`8Ool000IooaYcW0030nacW7>L01McW0<00=]cW0Qoo`001Woo6W>L 00<3k7>LLi`067>L0`00fW>L27oo0006OolHLi`20n`LLi`3003ILi`8Ool000IooaMcW0030nacW7>L 01ecW0<00=QcW0Qoo`001Woo5W>L00<3k7>LLi`07g>L0`00eg>L27oo0006OolFLi`00`?/LiacW00P Li`3003FLi`8Ool000IooaAcW083k2AcW0<00=EcW0Qoo`001Woo4g>L00<3k7>LLi`01G>L00<3k7>L Li`07G>L0`00e7>L27oo0006OolCLi`00`?/LiacW005Li`20n`OLi`3003CLi`8Ool000Iooa9cW003 0nacW7>L00McW083k1mcW0<00=9cW0Qoo`001Woo47>L0P?/2g>L0P?/7g>L0`00dG>L27oo0006Ool? Li`00`?/LiacW00L00ecW083k1mcW0<00L00<3k7>LLi`03g>L0P?/7g>L0`00cW>L27oo0006OolL01AcW083k1mcW0<00L00<3k7>LLi`0 =W>L0`00bg>L27oo0006Ool9Li`20n`jLi`3003:Li`8Ool000Ioo`QcW0030nacW7>L03]cW0<00L00<3k7>LLi`0?7>L0`00b7>L27oo0006Ool7Li`00`?/LiacW00nLi`30037Li`8 Ool000Ioo`QcW083k3mcW0<00L0P?/?W>L0`00aG>L27oo0006OolL00<3k7>LLi`0>W>L0`00`W>L 27oo0006OolALi`20n`kLi`30031Li`8Ool000Iooa=cW083k3YcW0<00<1cW0Qoo`001Woo5G>L0P?/ >G>L0`00_g>L27oo0006OolGLi`20n`hLi`3002nLi`8Ool000IooaUcW083k3McW0<00;ecW0Qoo`00 1Woo6g>L00<3k7>LLi`0=G>L0`00_7>L27oo0006OolLLi`20n`fLi`3002kLi`8Ool000IooaicW083 k3EcW0<00;YcW0Qoo`001Woo87>L00<3k7>LLi`0L0`00^G>L27oo0006OolQLi`20n`dLi`3002h Li`8Ool000Ioob=cW083k3=cW0<00;McW0Qoo`001Woo9G>L00<3k7>LLi`0L0`00]W>L27oo0006 OolVLi`20n`bLi`3002eLi`8Ool000IoobQcW083k35cW0<00;AcW0Qoo`001Woo:W>L0P?/<7>L0`00 /g>L27oo0006Ool/Li`20n`_Li`3002bLi`8Ool000IoobicW083k2icW0<00;5cW0Qoo`001Woo<7>L 00<3k7>LLi`0;7>L0`00/7>L27oo0006OolaLi`20n`]Li`3002_Li`8Ool000Iooc=cW083k2acW0<0 0:icW0Qoo`001Woo=G>L0P?/:g>L0`00[G>L27oo0006OolgLi`20n`ZLi`3002/Li`8Ool000IoocUc W083k2UcW0<00:]cW0Qoo`001Woo>g>L00<3k7>LLi`09g>L0`00ZW>L27oo0006OollLi`20n`XLi`3 002YLi`8Ool000IoocicW083k2McW0<00:QcW0Qoo`001Woo@7>L00<3k7>LLi`09G>L0`00Yg>L27oo 0006Oom1Li`20n`VLi`3002VLi`8Ool000Iood=cW083k2EcW0<00:EcW0Qoo`001WooAG>L00<3k7>L Li`08g>L0`00Y7>L27oo0006Oom6Li`20n`TLi`3002SLi`8Ool000IoodQcW083k2=cW0<00:9cW0Qo o`001WooBW>L0P?/8W>L0`00XG>L27oo0006OomL00<3k7>LLi`07W>L0`00WW>L27oo0006OomALi`20n`OLi`3002MLi`8 Ool000Iooe=cW083k1icW0<009acW0Qoo`001WooEG>L0P?/7G>L0`00Vg>L27oo0006OomGLi`20n`L Li`3002JLi`8Ool000IooeUcW083k1]cW0<009UcW0Qoo`001WooFg>L0P?/6W>L0`00V7>L27oo0006 OomMLi`20n`ILi`3002GLi`8Ool000IooemcW0030nacW7>L01McW0<009IcW0Qoo`001WooH7>L0P?/ 67>L0`00UG>L27oo0006OomRLi`20n`GLi`3002DLi`8Ool000IoofAcW0030nacW7>L01EcW0<009=c W0Qoo`001WooIG>L0P?/5W>L0`00TW>L27oo0006OomWLi`20n`ELi`3002ALi`8Ool000IoofUcW083 k1AcW0<0091cW0Qoo`001WooJg>L0P?/4g>L0`00Sg>L27oo0006Oom]Li`20n`BLi`3002>Li`8Ool0 00IoofmcW0030nacW7>L011cW0<008ecW0Qoo`001WooL7>L0P?/4G>L0`00S7>L27oo0006OombLi`2 0n`@Li`3002;Li`8Ool000IoogAcW0030nacW7>L00icW0<008YcW0Qoo`001WooMG>L0P?/3g>L0`00 RG>L27oo0006OomgLi`20n`>Li`30028Li`8Ool000IoogUcW0030nacW7>L00acW08008QcW0Qoo`00 1WooNW>L0P?/3G>L0P00Qg>L27oo0006OomlLi`20n`;Li`30026Li`8Ool000IoogicW083k0YcW0<0 08EcW0Qoo`001WooP7>L0P?/2G>L0`00Q7>L27oo0006Oon2Li`20n`8Li`30023Li`8Ool000IoohAc W0030nacW7>L00IcW0<0089cW0Qoo`001WooQG>L0P?/1g>L0`00PG>L27oo0006Oon7Li`20n`6Li`3 0020Li`8Ool000IoohUcW083k0EcW0<007mcW0Qoo`001WooRg>L0P?/17>L0`00OW>L27oo0006Oon= Li`20n`3Li`3001mLi`8Ool000IoohmcW083k09cW0<007acW0Qoo`001WooTG>L0P?/00AcW0000000 07]cW0Qoo`001WooTg>L00<3k7>L00000P00NW>L27oo0006OonDLi`20n`3001iLi`8Ool000IooiIc W083k08007QcW0Qoo`001WooV7>L00<3k0000000Mg>L27oo0006OonILi`20n`00`00LiacW01dLi`8 Ool000IooiYcW0030003k0?/07EcW0Qoo`001WooVg>L0P000P?/Lg>L27oo0006OonLLi`300020naa Li`8Ool000IooiecW0<00003Li`3k0?/06mcW0Qoo`001WooWW>L0`000W>L00<3k7>LLi`0K7>L27oo 0006OonOLi`30002Li`20na/Li`8Ool000Iooj1cW0<000=cW083k6YcW0Qoo`001WooXG>L0`0017>L 00<3k7>LLi`0Ig>L27oo0006OonRLi`30004Li`20naWLi`8Ool000Iooj=cW0<000EcW083k6EcW0Qo o`001WooY7>L0`001W>L00<3k7>LLi`0HW>L27oo0006OonULi`30006Li`20naRLi`8Ool000IoojIc W0<000McW083k61cW0Qoo`001WooYg>L0`0027>L00<3k7>LLi`0GG>L27oo0006OonXLi`30008Li`2 0naMLi`8Ool000IoojUcW0<000UcW083k5]cW0Qoo`001WooZW>L0`002W>L00<3k7>LLi`0F7>L27oo 0006Oon[Li`3000:Li`20naHLi`8Ool000IoojacW0<000]cW083k5IcW0Qoo`001Woo[G>L0`0037>L 0P?/E7>L27oo0006Oon^Li`3000=Li`20naBLi`8Ool000IoojmcW0<000icW083k51cW0Qoo`001Woo /7>L0`003g>L0P?/CW>L27oo0006OonaLi`3000@Li`20naL0`004W>L0P?/B7>L27oo0006OondLi`3000CLi`20na6Li`8Ool000IookEcW0<0 01AcW083k4AcW0Qoo`001Woo]W>L0`005G>L0P?/@W>L27oo0006OongLi`3000FLi`20na0Li`8Ool0 00IookQcW0<001McW0030nacW7>L03ecW0Qoo`001Woo^G>L0`005g>L0P?/?G>L27oo0006OonjLi`3 000HLi`20n`kLi`8Ool000Iook]cW0<001UcW0030nacW7>L03QcW0Qoo`001Woo_7>L0`006G>L0P?/ >7>L27oo0006OonmLi`3000JLi`20n`fLi`8Ool000IookicW0<001]cW0030nacW7>L03=cW0Qoo`00 1Woo_g>L0`006g>L0P?/L27oo0006Ooo0Li`3000LLi`20n`aLi`8Ool000Iool5cW0<001ecW003 0nacW7>L02icW0Qoo`001Woo`W>L0`007G>L0P?/;W>L27oo0006Ooo3Li`3000NLi`20n`/Li`8Ool0 00IoolAcW0<001mcW083k2YcW0Qoo`001WooaG>L0`0087>L0P?/:7>L27oo0006Ooo6Li`3000QLi`2 0n`VLi`8Ool000IoolMcW0<0029cW0030nacW7>L02=cW0Qoo`001Woob7>L0`008W>L0P?/8g>L27oo 0006Ooo9Li`3000SLi`20n`QLi`8Ool000IoolYcW0<002AcW083k1mcW0Qoo`001Woobg>L0`009G>L 0P?/7G>L27oo0006OooL01QcW0Qo o`001WoocW>L0`009g>L0P?/67>L27oo0006Ooo?Li`3000XLi`20n`FLi`8Ool000Ioom1cW0<002Uc W0030nacW7>L01=cW0Qoo`001WoodG>L0`00:G>L0P?/4g>L27oo0006OooBLi`3000ELi`00`?/Liac W004Li`20n`L009cW083k0mcW0030nacW7>L 00icW0Qoo`001Wooe7>L0`005G>L00<3k7>LLi`00P?/3g>L00<3k7>LLi`03g>L27oo0006OooELi`3 000ELi`30n`>Li`20n`BLi`8Ool000IoomIcW0<001AcW083k0icW0030nacW7>L019cW0Qoo`001Woo eg>L0`004g>L0`?/37>L00<3k7>LLi`04g>L27oo0006OooHLi`3000ALi`00`?/LiacW0020n`:Li`0 0`?/LiacW00DLi`8Ool000IoomUcW0<000mcW0030nacW7>L009cW083k0QcW0030nacW7>L01EcW0Qo o`001WoofW>L0`003G>L00<3k7>LLi`017>L0P?/1W>L00<3k7>LLi`05W>L27oo0006OooKLi`3000J Li`00`?/LiacW00GLi`8Ool000IoomacW0<001QcW0030nacW7>L01QcW0Qoo`001WoogG>L0`005g>L 00<3k7>LLi`067>L27oo0006OooNLi`3000ELi`00`?/LiacW00ILi`8Ool000IoommcW0<001=cW003 0nacW7>L01YcW0Qoo`001Wooh7>L0`004G>L00<3k7>LLi`06g>L27oo0006OooQLi`3000>Li`20n`N Li`8Ool000Ioon9cW0<000acW0030nacW7>L01icW0Qoo`001Woohg>L0`002W>L00<3k7>LLi`07g>L 27oo0006OooTLi`30008Li`00`?/LiacW00PLi`8Ool000IoonEcW0<000IcW0030nacW7>L025cW0Qo o`001WooiW>L0`0017>L00<3k7>LLi`08W>L27oo0006OooWLi`30002Li`00`?/LiacW00SLi`8Ool0 00IoonQcW0<000030nacW7>L02AcW0Qoo`001WoojG>L00<000?/00009W>L27oo0006OooZLi`00`00 LiacW00ULi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000Iooomc W1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L 27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool0 00IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Woo og>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`C Li`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qo o`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006 OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000Iooomc W1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L 27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool0 00IooomcW1=cW0Qoo`001Wooog>L4g>L27oo003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol0 0?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.874018, -0.853989, \ 0.00362693, 0.00362693}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Diagramma del taglio", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[frameb, pltO, pltQ, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic, PlotRange \[Rule] All];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.839656 0.960691 0.820415 0.960691 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .02381 m .02381 .97619 L .97619 .97619 L .97619 .02381 L F 0 g 2 Mabswid [ ] 0 setdash .83966 .82041 m .16034 .1411 L s 0 .4 1 r .5 Mabswid .76206 .89801 m .7423 .86266 L .72074 .8241 L .7005 .78789 L .68104 .75307 L .66031 .716 L .64037 .68033 L .61917 .6424 L .59874 .60586 L .57909 .57072 L .55819 .53332 L .53806 .49731 L .5187 .46269 L .4981 .42583 L .47826 .39035 L .45718 .35263 L .43686 .3163 L .41733 .28135 L .39653 .24416 L .37652 .20835 L .35525 .17031 L .33475 .13364 L .31503 .09837 L .29406 .06085 L .27489 .02656 L s .83966 .82041 m .83651 .82356 L .83308 .827 L .82985 .83022 L .82675 .83332 L .82345 .83662 L .82027 .8398 L .8169 .84317 L .81364 .84643 L .81051 .84956 L .80718 .85289 L .80398 .85609 L .8009 .85918 L .79761 .86246 L .79445 .86562 L .7911 .86898 L .78786 .87221 L .78475 .87532 L .78144 .87863 L .77825 .88182 L .77486 .88521 L .7716 .88847 L .76846 .89162 L .76511 .89496 L .76206 .89801 L s .16034 .1411 m .16499 .13646 L .17006 .13139 L .17482 .12663 L .1794 .12205 L .18427 .11718 L .18896 .11249 L .19394 .10751 L .19874 .1027 L .20336 .09808 L .20828 .09317 L .21301 .08844 L .21756 .08389 L .22241 .07904 L .22707 .07438 L .23203 .06942 L .2368 .06464 L .2414 .06005 L .24629 .05516 L .25099 .05045 L .25599 .04545 L .26081 .04063 L .26545 .036 L .27038 .03107 L .27489 .02656 L s .25837 .12459 m .25727 .12349 L .25607 .12229 L .25494 .12116 L .25386 .12007 L .2527 .11891 L .25159 .1178 L .2504 .11662 L .24927 .11548 L .24817 .11438 L .247 .11322 L .24588 .1121 L .2448 .11102 L .24365 .10987 L .24255 .10876 L .24137 .10758 L .24024 .10645 L .23915 .10536 L .23799 .1042 L .23687 .10309 L .23568 .1019 L .23454 .10076 L .23344 .09966 L .23227 .09849 L .2312 .09742 L s .78727 .84563 m .78617 .84452 L .78497 .84332 L .78384 .84219 L .78275 .84111 L .7816 .83995 L .78048 .83884 L .7793 .83766 L .77816 .83652 L .77707 .83542 L .7759 .83425 L .77478 .83313 L .7737 .83205 L .77255 .8309 L .77144 .8298 L .77027 .82862 L .76913 .82749 L .76804 .8264 L .76688 .82524 L .76577 .82412 L .76458 .82294 L .76344 .82179 L .76234 .82069 L .76117 .81952 L .7601 .81845 L s .7601 .84563 m .7612 .84452 L .7624 .84332 L .76353 .84219 L .76462 .84111 L .76577 .83995 L .76689 .83884 L .76807 .83766 L .76921 .83652 L .77031 .83542 L .77147 .83425 L .77259 .83313 L .77367 .83205 L .77482 .8309 L .77593 .8298 L .77711 .82862 L .77824 .82749 L .77933 .8264 L .78049 .82524 L .7816 .82412 L .78279 .82294 L .78393 .82179 L .78503 .82069 L .7862 .81952 L .78727 .81845 L s 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 288}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL0L00<1Wg>L0Il0b7>L27oo0006Oom6Li`0106OLiacW06Ob7>L27oo 0006Oom6Li`01@6OLiacW7>L0Il0ag>L27oo0006Oom4Li`20Il4Li`00`6OLiacW035Li`8Ool000Io od=cW0030ImcW7>L00EcW0030ImcW7>L0L00<1Wg>LLi`01W>L00<1Wg>LLi`0 `g>L27oo0006Oom2Li`00`6OLiacW007Li`00`6OLiacW033Li`8Ool000Iood1cW081W`]cW0030Imc W7>L0<9cW0Qoo`001Woo?g>L00<1Wg>LLi`02g>L00<1Wg>LLi`0`W>L27oo0006OoloLi`00`6OLiac W00L0<1cW0Qoo`001Woo?7>L00<1 Wg>LLi`047>L00<1Wg>LLi`0`7>L27oo0006OolkLi`00`6OLiacW00BLi`00`6OLiacW02oLi`8Ool0 00Iooc]cW0030ImcW7>L019cW0030ImcW7>L0;mcW0Qoo`001Woo>G>L0P6O5W>L00<1Wg>LLi`0_W>L 27oo0006OolhLi`00`6OLiacW00FLi`00`6OLiacW02nLi`8Ool000IoocQcW0030ImcW7>L01McW003 0ImcW7>L0;ecW0Qoo`001Woo=g>L00<1Wg>LLi`067>L00<1Wg>LLi`0_G>L27oo0006OoleLi`20IlL Li`00`6OLiacW02lLi`8Ool000IoocAcW0030ImcW7>L00EcW0030ImcW7>L01AcW0030ImcW7>L0;ac W0Qoo`001Woo=7>L00<1Wg>LLi`01G>L0P6O5W>L00<1Wg>LLi`0^g>L27oo0006OolcLi`00`6OLiac W007Li`20IlFLi`00`6OLiacW02jLi`8Ool000Iooc5cW081W`]cW081WaEcW0030ImcW7>L0;YcW0Qo o`001Woo<7>L00<1Wg>LLi`037>L0P6O5G>L00<1Wg>LLi`0^G>L27oo0006Ool`Li`00`6OLiacW00= Li`20IlDLi`00`6OLiacW02iLi`8Ool000IoobicW081Wa5cW081WaAcW0030ImcW7>L0;QcW0Qoo`00 1Woo;G>L00<1Wg>LLi`04W>L0P6O57>L00<1Wg>LLi`0]g>L27oo0006Ool]Li`00`6OLiacW00CLi`2 0IlCLi`00`6OLiacW02gLi`8Ool000IoobacW0030ImcW7>L02YcW0030ImcW7>L0;IcW0Qoo`001Woo :W>L0P6O;G>L00<1Wg>LLi`0]W>L27oo0006OolYLi`00`6OLiacW00^Li`00`6OLiacW02eLi`8Ool0 00IoobQcW0030001Wg>L02mcW0030ImcW7>L0;EcW0Qoo`001Woo9g>L00<0006O0000L00<1Wg>L Li`0]7>L27oo0006OolXLi`3000`Li`00`6OLiacW02dLi`8Ool000IoobUcW0<0031cW0030ImcW7>L 0;=cW0Qoo`001Woo:W>L0`00;g>L00<1Wg>LLi`0/g>L27oo0006Ool[Li`3000_Li`00`6OLiacW02b Li`8Ool000IoobacW0<002icW0030ImcW7>L0;9cW0Qoo`001Woo;G>L0`00;W>L00<1Wg>LLi`0/G>L 27oo0006Ool^Li`3000]Li`00`6OLiacW02aLi`8Ool000IoobmcW0<002ecW0030ImcW7>L0;1cW0Qo o`001Woo<7>L0`00;G>L00<1Wg>LLi`0[g>L27oo0006OolaLi`3000/Li`00`6OLiacW02_Li`8Ool0 00Iooc9cW0<002acW0030ImcW7>L0:icW0Qoo`001WooL0`00;7>L00<1Wg>LLi`0[G>L27oo0006 OoldLi`3000[Li`00`6OLiacW02]Li`8Ool000IoocEcW0<002]cW0030ImcW7>L0:acW0Qoo`001Woo =W>L0`00:W>L00<1Wg>LLi`0[7>L27oo0006OolgLi`3000ZLi`00`6OLiacW02[Li`8Ool000IoocQc W0<002YcW0030ImcW7>L0:YcW0Qoo`001Woo>G>L0`00:G>L00<1Wg>LLi`0ZW>L27oo0006OoljLi`3 000YLi`00`6OLiacW02YLi`8Ool000Iooc]cW0<002QcW0030ImcW7>L0:UcW0Qoo`001Woo?7>L0`00 :7>L00<1Wg>LLi`0Z7>L27oo0006OolmLi`3000WLi`00`6OLiacW02XLi`8Ool000IoocicW0<002Mc W0030ImcW7>L0:McW0Qoo`001Woo?g>L0`009W>L00<1Wg>LLi`0Yg>L27oo0006Oom0Li`3000VLi`0 0`6OLiacW02VLi`8Ool000Iood5cW0<002EcW0030ImcW7>L0:IcW0Qoo`001Woo@W>L0`009G>L00<1 Wg>LLi`0YG>L27oo0006Oom3Li`3000TLi`00`6OLiacW02ULi`8Ool000IoodAcW0<002AcW0030Imc W7>L0:AcW0Qoo`001WooAG>L0`008g>L00<1Wg>LLi`0Y7>L27oo0006Oom6Li`3000SLi`00`6OLiac W02SLi`8Ool000IoodMcW0<0029cW0030ImcW7>L0:=cW0Qoo`001WooB7>L0`008W>L00<1Wg>LLi`0 XW>L27oo0006Oom9Li`3000QLi`00`6OLiacW02RLi`8Ool000IoodYcW0<0025cW0030ImcW7>L0:5c W0Qoo`001WooBg>L0`008G>L00<1Wg>LLi`0X7>L27oo0006OomL09mcW0Qoo`001WooCW>L0`007g>L00<1Wg>LLi`0Wg>L27oo 0006Oom?Li`3000OLi`00`6OLiacW02NLi`8Ool000Iooe1cW0<001mcW0030ImcW7>L09ecW0Qoo`00 1WooDG>L0`007W>L00<1Wg>LLi`0WG>L27oo0006OomBLi`3000NLi`00`6OLiacW02LLi`8Ool000Io oe=cW0<001ecW0030ImcW7>L09acW0Qoo`001WooE7>L0`007G>L00<1Wg>LLi`0Vg>L27oo0006OomE Li`3000MLi`00`6OLiacW02JLi`8Ool000IooeIcW0<001acW0030ImcW7>L09YcW0Qoo`001WooEg>L 0`0077>L00<1Wg>LLi`0VG>L27oo0006OomHLi`3000KLi`00`6OLiacW02ILi`8Ool000IooeUcW0<0 01]cW0030ImcW7>L09QcW0Qoo`001WooFW>L0`006g>L00<1Wg>LLi`0Ug>L27oo0006OomKLi`3000J Li`00`6OLiacW02GLi`8Ool000IooeacW0<001YcW0030ImcW7>L09IcW0Qoo`001WooGG>L0`006G>L 00<1Wg>LLi`0UW>L27oo0006OomNLi`3000ILi`00`6OLiacW02ELi`8Ool000IooemcW0<001QcW003 0ImcW7>L09EcW0Qoo`001WooH7>L0`0067>L00<1Wg>LLi`0U7>L27oo0006OomQLi`3000GLi`00`6O LiacW02DLi`8Ool000Ioof9cW0<001McW0030ImcW7>L09=cW0Qoo`001WooHg>L0`005W>L00<1Wg>L Li`0Tg>L27oo0006OomTLi`3000FLi`00`6OLiacW02BLi`8Ool000IoofEcW0<001IcW0030ImcW7>L 095cW0Qoo`001WooIW>L0`005G>L00<1Wg>LLi`0TG>L27oo0006OomWLi`3000ELi`00`6OLiacW02@ Li`8Ool000IoofQcW0<001AcW0030ImcW7>L091cW0Qoo`001WooJG>L0`0057>L00<1Wg>LLi`0Sg>L 27oo0006OomZLi`3000CLi`00`6OLiacW02?Li`8Ool000Ioof]cW0<001=cW0030ImcW7>L08icW0Qo o`001WooK7>L0`004W>L00<1Wg>LLi`0SW>L27oo0006Oom]Li`3000BLi`00`6OLiacW02=Li`8Ool0 00IooficW0<0015cW0030ImcW7>L08ecW0Qoo`001WooKg>L0`004G>L00<1Wg>LLi`0S7>L27oo0006 Oom`Li`3000@Li`00`6OLiacW02L08]cW0Qoo`001Woo LW>L0`003g>L00<1Wg>LLi`0Rg>L27oo0006OomcLi`3000?Li`00`6OLiacW02:Li`8Ool000IoogAc W0<000icW0030ImcW7>L08YcW0Qoo`001WooMG>L0`003W>L00<1Wg>LLi`0RG>L27oo0006OomfLi`3 000=Li`00`6OLiacW029Li`8Ool000IoogMcW0<000ecW0030ImcW7>L08QcW0Qoo`001WooN7>L0`00 37>L00<1Wg>LLi`0R7>L27oo0006OomiLi`3000L08IcW0Qoo`001WooNg>L0`002g>L00<1Wg>LLi`0QW>L27oo0006OomlLi`3000;Li`0 0`6OLiacW025Li`8Ool000IoogecW0<000YcW0030ImcW7>L08EcW0Qoo`001WooOW>L0`002W>L00<1 Wg>LLi`0Q7>L27oo0006OomoLi`3000:Li`00`6OLiacW023Li`8Ool000Iooh1cW0<000UcW0030Imc W7>L08=cW0Qoo`001WooPG>L0`002G>L00<1Wg>LLi`0PW>L27oo0006Oon2Li`30008Li`00`6OLiac W022Li`8Ool000Iooh=cW0<000QcW0030ImcW7>L085cW0Qoo`001WooQ7>L0`0027>L00<1Wg>LLi`0 P7>L27oo0006Oon5Li`30007Li`00`6OLiacW020Li`8Ool000IoohIcW0<000McW0030ImcW7>L07mc W0Qoo`001WooQg>L0`001W>L00<1Wg>LLi`0Og>L27oo0006Oon8Li`20007Li`00`6OLiacW01nLi`8 Ool000IoohUcW08000McW0030ImcW7>L07ecW0Qoo`001WooRG>L0`001W>L00<1Wg>LLi`0OG>L27oo 0006Oon:Li`30006Li`00`6OLiacW01lLi`8Ool000Iooh]cW0<000EcW0030ImcW7>L07acW0Qoo`00 1WooS7>L0`001G>L00<1Wg>LLi`0Ng>L27oo0006Oon=Li`30005Li`00`6OLiacW01jLi`8Ool000Io ohicW0<000AcW0030ImcW7>L07YcW0Qoo`001WooSg>L0`0017>L00<1Wg>LLi`0NG>L27oo0006Oon@ Li`30003Li`00`6OLiacW01iLi`8Ool000Iooi5cW0<000=cW0030ImcW7>L07QcW0Qoo`001WooTW>L 0`000W>L00<1Wg>LLi`0N7>L27oo0006OonCLi`30002Li`00`6OLiacW01gLi`8Ool000IooiAcW0<0 0003Li`1Wg>L07QcW0Qoo`001WooUG>L0`0000=cW06OLi`0Mg>L27oo0006OonFLi`300000`6OLiac W01fLi`8Ool000IooiMcW0<000030ImcW7>L07EcW0Qoo`001WooV7>L0`0000<1Wg>LLi`0M7>L27oo 0006OonILi`200000`6OLiacW01dLi`8Ool000IooiYcW08000030ImcW7>L07=cW0Qoo`001WooVg>L 00<0006O0000M7>L27oo0006OonLLi`00`000Il0001cLi`8Ool000IooiecW0030001W`00079cW0Qo o`001WooWW>L00<1W`000000LG>L27oo0006OonOLi`00`6O0000001`Li`8Ool000IooimcW0040Il0 0000001_Li`8Ool000Iooj1cW0040Il00000001^Li`8Ool000Iooj1cW0030ImcW000008006ecW0Qo o`001WooXG>L00<1Wg>L00000P00K7>L27oo0006OonQLi`00`6OLiacW003001[Li`8Ool000Iooj9c W0030ImcW7>L00<006YcW0Qoo`001WooXW>L00@1Wg>LLiacW0<006UcW0Qoo`001WooXg>L00@1Wg>L LiacW0<006QcW0Qoo`001WooXg>L00<1Wg>LLi`00W>L0`00Ig>L27oo0006OonTLi`00`6OLiacW002 Li`3001VLi`8Ool000IoojAcW0030ImcW7>L00=cW0<006EcW0Qoo`001WooYG>L00<1Wg>LLi`00g>L 0`00I7>L27oo0006OonVLi`00`6OLiacW003Li`3001SLi`8Ool000IoojIcW0030ImcW7>L00AcW0<0 069cW0Qoo`001WooYg>L00<1Wg>LLi`017>L0`00HG>L27oo0006OonWLi`00`6OLiacW005Li`3001P Li`8Ool000IoojQcW0030ImcW7>L00EcW0<005mcW0Qoo`001WooZ7>L00<1Wg>LLi`01W>L0`00GW>L 27oo0006OonYLi`00`6OLiacW006Li`3001MLi`8Ool000IoojUcW0030ImcW7>L00McW0<005acW0Qo o`001WooZW>L00<1Wg>LLi`01g>L0`00Fg>L27oo0006OonZLi`00`6OLiacW008Li`3001JLi`8Ool0 00Iooj]cW0030ImcW7>L00QcW0<005UcW0Qoo`001Woo[7>L00<1Wg>LLi`027>L0`00F7>L27oo0006 Oon/Li`00`6OLiacW009Li`3001GLi`8Ool000IoojecW0030ImcW7>L00UcW0<005IcW0Qoo`001Woo [G>L00<1Wg>LLi`02W>L0`00EG>L27oo0006Oon^Li`00`6OLiacW00:Li`3001DLi`8Ool000Ioojic W0030ImcW7>L00]cW0<005=cW0Qoo`001Woo[g>L00<1Wg>LLi`02g>L0`00DW>L27oo0006Oon_Li`0 0`6OLiacW00L00acW0<0051cW0Qoo`001Woo/7>L00<1 Wg>LLi`03G>L0`00Cg>L27oo0006OonaLi`00`6OLiacW00=Li`3001>Li`8Ool000Iook9cW0030Imc W7>L00ecW0<004ecW0Qoo`001Woo/W>L00<1Wg>LLi`03W>L0`00C7>L27oo0006OoncLi`00`6OLiac W00>Li`3001;Li`8Ool000Iook=cW0030ImcW7>L00mcW0<004YcW0Qoo`001Woo]7>L00<1Wg>LLi`0 3g>L0`00BG>L27oo0006OoneLi`00`6OLiacW00?Li`30018Li`8Ool000IookEcW0030ImcW7>L011c W0<004McW0Qoo`001Woo]W>L00<1Wg>LLi`047>L0`00AW>L27oo0006OonfLi`00`6OLiacW00ALi`3 0015Li`8Ool000IookMcW0030ImcW7>L015cW0<004AcW0Qoo`001Woo^7>L00<1Wg>LLi`04G>L0`00 @g>L27oo0006OonhLi`00`6OLiacW00BLi`30012Li`8Ool000IookUcW0030ImcW7>L019cW0<0045c W0Qoo`001Woo^G>L00<1Wg>LLi`04g>L0`00@7>L27oo0006OonjLi`00`6OLiacW00CLi`3000oLi`8 Ool000IookYcW0030ImcW7>L01AcW0<003icW0Qoo`001Woo^g>L00<1Wg>LLi`057>L0`00?G>L27oo 0006OonkLi`00`6OLiacW00ELi`3000lLi`8Ool000IookacW0030ImcW7>L01EcW0<003]cW0Qoo`00 1Woo_7>L00<1Wg>LLi`05W>L0`00>W>L27oo0006OonmLi`00`6OLiacW00FLi`3000iLi`8Ool000Io okicW0030ImcW7>L01IcW0<003QcW0Qoo`001Woo_W>L00<1Wg>LLi`05g>L0`00=g>L27oo0006Oono Li`00`6OLiacW00GLi`3000fLi`8Ool000IookmcW0030ImcW7>L01QcW0<003EcW0Qoo`001Woo`7>L 00<1Wg>LLi`067>L0`00=7>L27oo0006Ooo1Li`00`6OLiacW00HLi`3000cLi`8Ool000Iool5cW003 0ImcW7>L01UcW0<0039cW0Qoo`001Woo`W>L00<1Wg>LLi`06G>L0`00L27oo0006Ooo2Li`00`6O LiacW00JLi`3000`Li`8Ool000Iool=cW0030ImcW7>L01YcW0<002mcW0Qoo`001Woo`g>L00<1Wg>L Li`06g>L0`00;W>L27oo0006Ooo4Li`00`6OLiacW00KLi`3000]Li`8Ool000IoolAcW0030ImcW7>L 01acW0<002acW0Qoo`001WooaG>L00<1Wg>LLi`077>L0`00:g>L27oo0006Ooo5Li`00`6OLiacW00M Li`3000ZLi`8Ool000IoolIcW0030ImcW7>L01ecW0<002UcW0Qoo`001WooaW>L00<1Wg>LLi`07W>L 0`00:7>L27oo0006Ooo7Li`00`6OLiacW00:Li`00`6OLiacW004Li`00`6OLiacW00:Li`3000WLi`8 Ool000IoolMcW0030ImcW7>L00YcW081W`AcW081W`ecW0030001W`0002IcW0Qoo`001Woob7>L00<1 Wg>LLi`02W>L0P6O0g>L00<1Wg>LLi`03G>L00<1Wg>LLi`09G>L27oo0006Ooo9Li`00`6OLiacW00: Li`20Il00g>L0ImcW00>Li`00`6OLiacW00VLi`8Ool000IoolUcW0030ImcW7>L00]cW081W`mcW003 0ImcW7>L02McW0Qoo`001WoobW>L00<1Wg>LLi`02W>L0`6O3G>L00<1Wg>LLi`0:7>L27oo0006Ooo; Li`00`6OLiacW008Li`0106OLiacW06O37>L00<1Wg>LLi`0:G>L27oo0006Ooo;Li`00`6OLiacW007 Li`00`6OLiacW002Li`00`6OLiacW007Li`20Il/Li`8Ool000IoolacW0030ImcW7>L00EcW0030Imc W7>L00AcW0030ImcW7>L00EcW0030ImcW7>L02acW0Qoo`001Wooc7>L00<1Wg>LLi`04g>L00<1Wg>L Li`0;G>L27oo0006Ooo=Li`00`6OLiacW00ALi`00`6OLiacW00^Li`8Ool000IoolicW0030ImcW7>L 00mcW0030ImcW7>L02mcW0Qoo`001WoocW>L00<1Wg>LLi`03W>L00<1Wg>LLi`0<7>L27oo0006Ooo? Li`00`6OLiacW00L00acW0030ImcW7>L035c W0Qoo`001Wood7>L00<1Wg>LLi`02W>L00<1Wg>LLi`0L27oo0006Ooo@Li`00`6OLiacW009Li`0 0`6OLiacW00cLi`8Ool000Ioom5cW0030ImcW7>L00McW0030ImcW7>L03AcW0Qoo`001WoodG>L00<1 Wg>LLi`01W>L00<1Wg>LLi`0=G>L27oo0006OooBLi`00`6OLiacW004Li`00`6OLiacW00fLi`8Ool0 00Ioom9cW0030ImcW7>L009cW081WcUcW0Qoo`001Woodg>L00@1Wg>LLi`1Wc]cW0Qoo`001Woodg>L 00<1Wg>L0Il0?7>L27oo0006OooDLi`00`6OLiacW00kLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L 4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8 Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`00 1Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006Oooo Li`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=c W0Qoo`001Wooog>L4g>L27oo0006OoooLi`CLi`8Ool000IooomcW1=cW0Qoo`001Wooog>L4g>L27oo 003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {287, 0}} -> {-0.874018, -0.853989, \ 0.00362693, 0.00362693}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Diagramma del momento", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[frameb, pltO, pltM, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic, PlotRange \[Rule] All];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .99788 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.839946 0.958652 0.818673 0.958652 [ [ 0 0 0 0 ] [ 1 .99788 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02583 .02376 m .02583 .97412 L .97619 .97412 L .97619 .02376 L F 0 g 2 Mabswid [ ] 0 setdash .83995 .81867 m .16208 .1408 L s .8 0 1 r .5 Mabswid .83995 .81867 m .83775 .7941 L .83482 .7688 L .82654 .7171 L .81663 .67283 L .80357 .62823 L .78854 .58776 L .76991 .54738 L .7494 .51105 L .72728 .47849 L .70117 .44642 L .67354 .41804 L .64465 .39307 L .6114 .36897 L .57696 .34821 L .53774 .32876 L .49741 .31256 L .45626 .29934 L .40992 .28781 L .36285 .27919 L .33606 .2755 L .31016 .27269 L .29739 .27156 L .28373 .27053 L .27079 .26972 L .25886 .26911 L .24589 .26859 L .23917 .26838 L .23182 .26819 L .22499 .26805 L .22198 .26801 L .21864 .26796 L .21571 .26793 L .21254 .26791 L .21079 .2679 L .20919 .26789 L .20765 .26789 L .20603 .26788 L .20427 .26788 L .20328 .26788 L .20237 .26788 L .20068 .26789 L .1989 .26789 L .1973 .2679 L .1958 .26791 L .19239 .26793 L .18869 .26797 L .18531 .26802 L .17766 .26815 L .17109 .2683 L Mistroke .1639 .2685 L .15071 .26895 L .12119 .27041 L .08909 .27264 L .02381 .27907 L Mfstroke .83995 .81867 m .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L .83995 .81867 L s .16208 .1408 m .15647 .14641 L .15035 .15253 L .14461 .15828 L .13908 .1638 L .1332 .16968 L .12754 .17534 L .12152 .18136 L .11572 .18716 L .11015 .19273 L .10421 .19867 L .0985 .20438 L .09301 .20987 L .08716 .21572 L .08153 .22135 L .07555 .22733 L .06978 .2331 L .06424 .23864 L .05833 .24455 L .05265 .25023 L .04662 .25626 L .0408 .26208 L .0352 .26768 L .02925 .27363 L .02381 .27907 L s 0 0 m 1 0 L 1 .99788 L 0 .99788 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 287.375}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo 0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000Mo oomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L 4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8 Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`00 1gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007Oooo Li`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19c W0Qoo`001gooog>L4W>L27oo0007OolWLi`00`00LiacW03WLi`8Ool000MoobIcW003001T7`000>Qc W0Qoo`001goo9G>L0V@O0`00ig>L27oo0007OolTLi`016@OLiacW7>L0`00iW>L27oo0007OolTLi`0 0f@OLiacW002Li`3003ULi`8Ool000Moob=cW003I1mcW7>L00AcW0<00>AcW0Qoo`001goo8W>L00=T 7g>LLi`01W>L0`00hg>L27oo0007OolPLi`2I1l:Li`3003RLi`8Ool000MooamcW003I1mcW7>L00]c W0<00>5cW0Qoo`001goo7g>L00=T7g>LLi`037>L0`00h7>L27oo0007OolMLi`2I1l@Li`3003OLi`8 Ool000MooaacW003I1mcW7>L015cW0<00=icW0Qoo`001goo6g>L00=T7g>LLi`04g>L0`00gG>L27oo 0007OolJLi`00f@OLiacW00ELi`3003LLi`8Ool000MooaYcW003I1mcW7>L01IcW0<00=]cW0Qoo`00 1goo67>L0V@O6W>L0`00fW>L27oo0007OolGLi`00f@OLiacW00KLi`3003ILi`8Ool000MooaIcW003 I1mcW7>L01ecW0<00=QcW0Qoo`001goo5G>L00=T7g>LLi`07g>L0`00eg>L27oo0007OolELi`00f@O LiacW00PLi`3003FLi`8Ool000Mooa=cW09T7bAcW0<00=EcW0Qoo`001goo4W>L00=T7g>LLi`09G>L 0`00e7>L27oo0007OolBLi`00f@OLiacW00VLi`3003CLi`8Ool000Mooa5cW003I1mcW7>L02QcW0<0 0=9cW0Qoo`001goo47>L00=T7g>LLi`0:W>L0`00dG>L27oo0007Ool>Li`2I1l^Li`3003@Li`8Ool0 00Moo`ecW003I1mcW7>L02mcW0<00L00=T7g>LLi`0<7>L0`00cW>L27oo0007 OolL03AcW0<00L0V@O>7>L0`00bg>L27oo0007Ool8Li`00f@OLiacW00iLi`3003:Li`8Ool000Moo`QcW003I1mc W7>L03YcW0<00L00=T7g>LLi`0?7>L0`00b7>L27oo0007Ool6Li`00f@OLiac W00nLi`30037Li`8Ool000Moo`AcW09T7d9cW0<00L00=T7g>LLi`0@g>L0`00 aG>L27oo0007Ool3Li`00f@OLiacW00JLi`UI1l5Li`30034Li`8Ool000Moo`9cW003I1mcW7>L00Uc W19T7bEcW15T7k]cW0Qoo`001goo00AcW6@OLiacW0YT7cicW0<000McW0MT7kAcW0Qoo`001Woo1F@O BG>L0`003G>L1f@O[G>L27oo0007Oom>Li`3000CLi`4I1nYLi`8Ool000MoodmcW0<001IcW0AT7jEc W0Qoo`001gooD7>L0`006G>L1F@OX7>L27oo0007OomALi`3000MLi`4I1nLLi`8Ool000Mooe9cW0<0 021cW0AT7iQcW0Qoo`001gooDg>L0`008g>L16@OU7>L27oo0007OomDLi`3000VLi`3I1nALi`8Ool0 00MooeEcW0<002QcW0=T7hicW0Qoo`001gooEW>L0`00:W>L0f@ORg>L27oo0007OomGLi`3000/Li`3 I1n8Li`8Ool000MooeQcW0<002icW0=T7hEcW0Qoo`001gooFG>L0`00<7>L0f@OPW>L27oo0007OomJ Li`3000bLi`3I1moLi`8Ool000Mooe]cW0<003AcW09T7gecW0Qoo`001gooG7>L0`00=G>L0V@ONg>L 27oo0007OomMLi`3000fLi`2I1miLi`8Ool000MooeicW0<003McW09T7gMcW0Qoo`001gooGg>L0`00 >7>L0V@OMG>L27oo0007OomPLi`3000iLi`2I1mcLi`8Ool000Moof5cW0<003YcW003I1mcW7>L071c W0Qoo`001gooHW>L0`00>W>L0V@OL7>L27oo0007OomSLi`3000kLi`2I1m^Li`8Ool000MoofAcW0<0 03acW003I1mcW7>L06]cW0Qoo`001gooIG>L0`00?7>L0V@OJg>L27oo0007OomVLi`3000mLi`2I1mY Li`8Ool000MoofMcW0<003icW003I1mcW7>L06IcW0Qoo`001gooJ7>L0`00?W>L0V@OIW>L27oo0007 OomYLi`3000oLi`00f@OLiacW01SLi`8Ool000MoofYcW0<003mcW003I1mcW7>L069cW0Qoo`001goo Jg>L0`00?g>L0V@OHW>L27oo0007Oom/Li`30010Li`00f@OLiacW01OLi`8Ool000MoofecW0<0041c W09T7emcW0Qoo`001gooKW>L0`00@G>L00=T7g>LLi`0G7>L27oo0007Oom_Li`30011Li`00f@OLiac W01KLi`8Ool000Moog1cW0<0045cW003I1mcW7>L05YcW0Qoo`001gooLG>L0`00@G>L00=T7g>LLi`0 FG>L27oo0007OombLi`30011Li`2I1mILi`8Ool000Moog=cW0<0049cW003I1mcW7>L05IcW0Qoo`00 1gooM7>L0`00@W>L00=T7g>LLi`0EG>L27oo0007OomeLi`30012Li`00f@OLiacW01DLi`8Ool000Mo ogIcW0<0049cW003I1mcW7>L05=cW0Qoo`001gooMg>L0`00@W>L00=T7g>LLi`0DW>L27oo0007Oomh Li`30012Li`00f@OLiacW01ALi`8Ool000MoogUcW0<0049cW003I1mcW7>L051cW0Qoo`001gooNW>L 0`00@W>L00=T7g>LLi`0Cg>L27oo0007OomkLi`30012Li`00f@OLiacW01>Li`8Ool000MoogacW0<0 049cW003I1mcW7>L04ecW0Qoo`001gooOG>L0`00@W>L00=T7g>LLi`0C7>L27oo0007OomnLi`30012 Li`00f@OLiacW01;Li`8Ool000MoogmcW0<0049cW003I1mcW7>L04YcW0Qoo`001gooP7>L0`00@G>L 00=T7g>LLi`0BW>L27oo0007Oon1Li`30011Li`00f@OLiacW019Li`8Ool000Mooh9cW0<0045cW003 I1mcW7>L04QcW0Qoo`001gooPg>L0`00@G>L00=T7g>LLi`0Ag>L27oo0007Oon4Li`30010Li`00f@O LiacW017Li`8Ool000MoohEcW0<0041cW003I1mcW7>L04IcW0Qoo`001gooQW>L0`00@7>L00=T7g>L Li`0AG>L27oo0007Oon7Li`4000oLi`00f@OLiacW014Li`8Ool000MoohQcW0@003icW003I1mcW7>L 04AcW0Qoo`001gooRW>L0`00?W>L00=T7g>LLi`0@g>L27oo0007Oon;Li`3000nLi`00f@OLiacW012 Li`8Ool000MoohacW0<003ecW003I1mcW7>L049cW0Qoo`001gooSG>L0`00?G>L00=T7g>LLi`0@G>L 27oo0007Oon>Li`3000mLi`00f@OLiacW010Li`8Ool000MoohmcW0<003ecW003I1mcW7>L03mcW0Qo o`001gooT7>L0`00?7>L00=T7g>LLi`0?g>L27oo0007OonALi`3000lLi`00f@OLiacW00nLi`8Ool0 00Mooi9cW0<003]cW003I1mcW7>L03icW0Qoo`001gooTg>L0`00>g>L00=T7g>LLi`0?G>L27oo0007 OonDLi`3000jLi`00f@OLiacW00mLi`8Ool000MooiEcW0<003YcW003I1mcW7>L03acW0Qoo`001goo UW>L0`00>G>L00=T7g>LLi`0?7>L27oo0007OonGLi`3000iLi`00f@OLiacW00kLi`8Ool000MooiQc W0<003QcW003I1mcW7>L03]cW0Qoo`001gooVG>L0`00>7>L00=T7g>LLi`0>W>L27oo0007OonJLi`3 000gLi`00f@OLiacW00jLi`8Ool000Mooi]cW0<003McW003I1mcW7>L03UcW0Qoo`001gooW7>L0`00 =W>L00=T7g>LLi`0>G>L27oo0007OonMLi`3000fLi`00f@OLiacW00hLi`8Ool000MooiicW0<003Ec W003I1mcW7>L03QcW0Qoo`001gooWg>L0`00=G>L00=T7g>LLi`0=g>L27oo0007OonPLi`3000dLi`0 0f@OLiacW00gLi`8Ool000Mooj5cW0<003AcW003I1mcW7>L03IcW0Qoo`001gooXW>L0`00L00=T 7g>LLi`0=W>L27oo0007OonSLi`3000cLi`00f@OLiacW00eLi`8Ool000MoojAcW0<0039cW003I1mc W7>L03EcW0Qoo`001gooYG>L0`00L00=T7g>LLi`0=7>L27oo0007OonVLi`3000aLi`00f@OLiac W00dLi`8Ool000MoojMcW0<0035cW003I1mcW7>L03=cW0Qoo`001gooZ7>L0`00<7>L00=T7g>LLi`0 L27oo0007OonYLi`3000`Li`00f@OLiacW00bLi`8Ool000MoojYcW0<002mcW003I1mcW7>L039c W0Qoo`001gooZg>L0`00;W>L00=T7g>LLi`0L27oo0007Oon/Li`3000^Li`00f@OLiacW00aLi`8 Ool000MoojecW0<002ecW003I1mcW7>L035cW0Qoo`001goo[W>L0`00;G>L00=T7g>LLi`0<7>L27oo 0007Oon_Li`3000/Li`00f@OLiacW00`Li`8Ool000Mook1cW0<002]cW003I1mcW7>L031cW0Qoo`00 1goo/G>L0`00:g>L00=T7g>LLi`0;g>L27oo0007OonbLi`3000ZLi`00f@OLiacW00_Li`8Ool000Mo ok=cW0<002UcW003I1mcW7>L02mcW0Qoo`001goo]7>L0`00:G>L00=T7g>LLi`0;W>L27oo0007Oone Li`3000XLi`00f@OLiacW00^Li`8Ool000MookIcW0<002McW003I1mcW7>L02icW0Qoo`001goo]g>L 0`009g>L00=T7g>LLi`0;G>L27oo0007OonhLi`3000VLi`00f@OLiacW00]Li`8Ool000MookUcW0<0 02EcW003I1mcW7>L02ecW0Qoo`001goo^W>L0`0097>L00=T7g>LLi`0;G>L27oo0007OonkLi`3000T Li`00f@OLiacW00/Li`8Ool000MookacW0<002=cW003I1mcW7>L02acW0Qoo`001goo_G>L0`008W>L 00=T7g>LLi`0;7>L27oo0007OonnLi`3000RLi`00f@OLiacW00[Li`8Ool000MookmcW0<0025cW003 I1mcW7>L02]cW0Qoo`001goo`7>L0`0087>L00=T7g>LLi`0:g>L27oo0007Ooo1Li`3000OLi`00f@O LiacW00[Li`8Ool000Mool9cW0<001mcW003I1mcW7>L02YcW0Qoo`001goo`g>L0`007W>L00=T7g>L Li`0:W>L27oo0007Ooo4Li`3000MLi`00f@OLiacW00ZLi`8Ool000MoolEcW0<001acW003I1mcW7>L 02YcW0Qoo`001gooaW>L0`0077>L00=T7g>LLi`0:G>L27oo0007Ooo7Li`3000KLi`00f@OLiacW00Y Li`8Ool000MoolQcW0<001YcW003I1mcW7>L02UcW0Qoo`001goobG>L0`006G>L00=T7g>LLi`0:G>L 27oo0007Ooo:Li`3000ILi`00f@OLiacW00XLi`8Ool000Mool]cW0<001QcW003I1mcW7>L02QcW0Qo o`001gooc7>L0`005g>L00=T7g>LLi`0:7>L27oo0007Ooo=Li`3000FLi`00f@OLiacW00XLi`8Ool0 00MoolicW0<001EcW003I1mcW7>L02QcW0Qoo`001goocg>L0`0057>L00=T7g>LLi`0:7>L27oo0007 Ooo@Li`3000DLi`00f@OLiacW00WLi`8Ool000Moom5cW0<001=cW003I1mcW7>L02McW0Qoo`001goo dW>L0`004W>L00=T7g>LLi`09g>L27oo0007OooCLi`3000ALi`00f@OLiacW00WLi`8Ool000MoomAc W0<0011cW003I1mcW7>L02McW0Qoo`001gooeG>L0`003g>L00=T7g>LLi`09g>L27oo0007OooFLi`3 000>Li`00f@OLiacW00WLi`8Ool000MoomMcW0<000ecW003I1mcW7>L02McW0Qoo`001goof7>L0`00 3G>L00=T7g>LLi`09W>L27oo0007OooILi`3000L02IcW0Qoo`001goofg>L0`002W>L00=T7g>LLi`09W>L27oo0007OooLLi`30009Li`0 0f@OLiacW00VLi`8Ool000MoomecW0<000QcW003I1mcW7>L02IcW0Qoo`001googW>L0`001g>L00=T 7g>LLi`09W>L27oo0007OooOLi`30007Li`00f@OLiacW00ULi`8Ool000Moon1cW0<000IcW003I1mc W7>L02EcW0Qoo`001goohG>L0`001G>L00=T7g>LLi`09G>L27oo0007OooRLi`30004Li`00f@OLiac W00ULi`8Ool000Moon=cW0<000=cW003I1mcW7>L02EcW0Qoo`001gooi7>L0`000W>L00=T7g>LLi`0 9G>L27oo0007OooULi`300000g>LI1mcW00VLi`8Ool000MoonIcW0<00003LiaT7g>L02EcW0Qoo`00 1gooig>L0`0000=T7g>LLi`097>L27oo0007OooXLi`200000f@OLiacW00TLi`8Ool000MoonUcW003 001T7`0002EcW0Qoo`001goojW>L00<007>LLi`097>L27oo0007OoooLi`BLi`8Ool000MooomcW19c W0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo 0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000Mo oomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L 4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8 Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`00 1gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007Oooo Li`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19c W0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo 0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000Mo oomcW19cW0Qoo`001gooog>L4W>L27oo0007OoooLi`BLi`8Ool000MooomcW19cW0Qoo`00ogoo8Goo 003oOolQOol00?moob5oo`00ogoo8Goo003oOolQOol00?moob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {286.375, 0}} -> {-0.876209, -0.853989, \ 0.00363485, 0.00363485}}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Salvataggio figure in formato EPS", FontColor->RGBColor[1, 0, 0]]], "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Directory[]\)], "Input"], Cell[BoxData[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-11a\\outmath"\)], "Output"] }, Open ]], Cell[BoxData[ \(\(phframe = Graphics[{GrayLevel[1], {Point[xLowerL], Point[xUpperR]}}] /. datinum;\)\)], "Input"], Cell[BoxData[ \(Do[Display["\" <> ToString[it] <> "\<.eps\>", Show[grNQM[it], ImageSize \[Rule] {320, Automatic}, DisplayFunction \[Rule] Identity], "\"], {it, 1, travi}]\)], "Input"], Cell[BoxData[ \(Do[Display["\" <> ToString[it] <> "\<.eps\>", Show[gruv\[Theta][it], ImageSize \[Rule] {320, Automatic}, DisplayFunction \[Rule] Identity], "\"], {it, 1, travi}]\)], "Input"], Cell["Adattare ImageSize nei comandi seguenti", "SmallText", CellFrame->True, Background->GrayLevel[0.849989]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{sc = 100}, \[IndentingNewLine]{imageW = sc*\((xUpperR - xLowerL)\)\_\(\(\[LeftDoubleBracket]\)\(1\)\(\ \[RightDoubleBracket]\)\) // Floor, \[IndentingNewLine]imageH = sc*\((xUpperR - xLowerL)\)\_\(\(\[LeftDoubleBracket]\)\(2\)\(\ \[RightDoubleBracket]\)\) // Floor}]\)], "Input"], Cell[BoxData[ \({99, 99}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(Display["\", Show[phframe, pltO, pltOv, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"], Cell[BoxData[ \(\(Display["\", Show[phframe, pltOx, pltOax, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"], Cell[BoxData[ \(\(Display["\", Show[phframe, pltO, pltOs, pltD, pltDs, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"], Cell[BoxData[ \(\(Display["\", Show[phframe, pltO, pltN, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"], Cell[BoxData[ \(\(Display["\", Show[phframe, pltO, pltQ, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"], Cell[BoxData[ \(\(Display["\", Show[phframe, pltO, pltM, ImageSize \[Rule] {imageW, imageH}, AspectRatio \[Rule] Automatic, DisplayFunction \[Rule] Identity, PlotRange \[Rule] All], "\"];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Salvataggio espressioni in formato", FontColor->RGBColor[1, 0, 0]], " ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]] }], "Section"], Cell[CellGroupData[{ Cell["Definizioni generali", "Subsection"], Cell[CellGroupData[{ Cell[BoxData[ \(Directory[]\)], "Input"], Cell[BoxData[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-11a\\outmath"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \({\[Alpha], b, c, d, f, L, M, YA, YJ}\)], "Input"], Cell[BoxData[ \({\[Alpha], b, c, d, f, L, M, YA, YJ}\)], "Output"] }, Open ]], Cell["\<\ Controllare che le variabili precedenti non abbiano un valore. Per sicurezza \ vengono utilizzati gli apici.\ \>", "SmallText"], Cell[BoxData[ \(myTeXForm[exp_] := Block[{\[Alpha]}, TeXForm[Evaluate[ exp /. {\[ScriptA] \[Rule] \[Alpha], \[ScriptB] \[Rule] b, \[ScriptC] \[Rule] c, \[ScriptD] \[Rule] d, \[ScriptF] \[Rule] f, \[ScriptCapitalL] \[Rule] L, \[ScriptCapitalM] \[Rule] M, \[ScriptCapitalY]\[ScriptCapitalA]\ \[Rule] YA\ , \ \[ScriptCapitalY]\[ScriptCapitalJ] \[Rule] YJ}]]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Definition[extraSimplify]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {GridBox[{ {\(extraSimplify = #1 &\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnWidths->0.999, ColumnAlignments->{Left}]} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], Definition[ extraSimplify], Editable->False]], "Output"] }, Open ]], Cell["\<\ Questa funzione serve ad apporre la numerazione delle travi ai simboli delle \ variabili [ATTENZIONE al fatto che tale definizione potrebbe dar luogo a LOOP senza \ fine nel caso di una sola trave]\ \>", "SmallText"], Cell[BoxData[ \(newsym[var_[n_]] := If[travi > 1, Superscript[var, "\<\\bn{\>" <> ToString[n] <> "\<}\>"], var]\)], "Input"], Cell["\<\ La seconda definizione di newsym \[EGrave] utilizzata per costruire le \ espressioni di forze e momenti alle estremit\[AGrave] (bd \[EGrave] pi\ \[UGrave] o meno)\ \>", "SmallText"], Cell[BoxData[ \(newsym[var_[n_, bd_]] := If[travi > 1, Superscript[ var, "\<\\bbn{\>" <> ToString[n] <> "\<}{\>" <> bd <> "\<}\>"], var^bd]\)], "Input"], Cell[BoxData[ \(\(newsymlist1 = {sNo[bn_] \[RuleDelayed] newsym[sNo[bn]], sQo[bn_] \[RuleDelayed] newsym[sQo[bn]], sMo[bn_] \[RuleDelayed] newsym[sMo[bn]], sN[bn_] \[RuleDelayed] newsym[sN[bn]], sQ[bn_] \[RuleDelayed] newsym[sQ[bn]], sM[bn_] \[RuleDelayed] newsym[sM[bn]]};\)\)], "Input"], Cell[BoxData[ \(\(newsymlist2 = {u\_1[bn_] \[RuleDelayed] newsym[u1[bn]], u\_2[bn_] \[RuleDelayed] newsym[u2[bn]], \[Theta][bn_] \[RuleDelayed] newsym[theta[bn]]};\)\)], "Input"], Cell[BoxData[ \(\(newsymlist3 = {sNo[bn_] \[RuleDelayed] newsym[sNo[bn]], sQo[bn_] \[RuleDelayed] newsym[sQo[bn]], sMo[bn_] \[RuleDelayed] newsym[sMo[bn]], uo\_1[bn_] \[RuleDelayed] newsym[u1o[bn]], uo\_2[bn_] \[RuleDelayed] newsym[u2o[bn]], \[Theta]o[bn_] \[RuleDelayed] newsym[thetao[bn]], u\_1[bn_] \[RuleDelayed] newsym[u1[bn]], u\_2[bn_] \[RuleDelayed] newsym[u2[bn]], \[Theta][bn_] \[RuleDelayed] newsym[theta[bn]]};\)\)], "Input"], Cell[BoxData[ \(\(newsymlist4 = {sNo[bn_] \[RuleDelayed] newsym[sNo[bn]], sQo[bn_] \[RuleDelayed] newsym[sQo[bn]], sMo[bn_] \[RuleDelayed] newsym[sMo[bn]]};\)\)], "Input"], Cell[BoxData[ \(\(newsymlist5 = {sNo[bn_] \[RuleDelayed] newsym[sNo[bn]], sQo[bn_] \[RuleDelayed] newsym[sQo[bn]], sMo[bn_] \[RuleDelayed] newsym[sMo[bn]], uo\_1[bn_] \[RuleDelayed] newsym[u1o[bn]], uo\_2[bn_] \[RuleDelayed] newsym[u2o[bn]], \[Theta]o[bn_] \[RuleDelayed] newsym[thetao[bn]]};\)\)], "Input"], Cell[BoxData[ \(\(newsymlist6 = {s[bn_, bd_] \[RuleDelayed] newsym[s[bn, bd]], m[bn_, bd_] \[RuleDelayed] newsym[m[bn, bd]], s\_1[bn_, bd_] \[RuleDelayed] newsym[s\_1[bn, bd]], s\_2[bn_, bd_] \[RuleDelayed] newsym[s\_2[bn, bd]]};\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " delle equazioni di bilancio" }], "Subsection"], Cell["\<\ Notare la tecnica utilizzata per generare la forma TEX di equazioni, \ separando i due mebri.\ \>", "SmallText"], Cell[BoxData[ \(texBil1[i_, j_] := myTeXForm[ Evaluate[\(eqbilt[i]\)\_\(\(\[LeftDoubleBracket]\)\(1, j\)\(\ \[RightDoubleBracket]\)\) // Simplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texBil2[i_, j_] := myTeXForm[ Evaluate[\(eqbilt[i]\)\_\(\(\[LeftDoubleBracket]\)\(2, j\)\(\ \[RightDoubleBracket]\)\) // Simplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texBil3[i_, j_] := myTeXForm[ Evaluate[\(eqbilt[i]\)\_\(\(\[LeftDoubleBracket]\)\(3, j\)\(\ \[RightDoubleBracket]\)\) // Simplify] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist1}, Do[\[IndentingNewLine]WriteString[stFile, texBil1[i, 1], "\< &= \>", texBil1[i, 2]]; WriteString[ stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texBil2[i, 1], "\< &= \>", texBil2[i, 2]]; WriteString[ stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texBil3[i, 1], "\< &= \>", texBil3[i, 2]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expBil.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " degli integrali delle equazioni di bilancio" }], "Subsection"], Cell[BoxData[ \(texNin[i_] := myTeXForm[ Evaluate[\(\(sN[i]\)[\[Zeta]] /. bulksol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texQin[i_] := myTeXForm[ Evaluate[\(\(sQ[i]\)[\[Zeta]] /. bulksol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texMin[i_] := myTeXForm[ Evaluate[\(\(sM[i]\)[\[Zeta]] /. bulksol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texNn[i_] := myTeXForm[\(sN[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texQn[i_] := myTeXForm[\(sQ[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texMn[i_] := myTeXForm[\(sM[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist1}, Do[\[IndentingNewLine]WriteString[stFile, texNn[i], "\< &= \>", texNin[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texQn[i], "\< &= \>", texQin[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texMn[i], "\< &= \>", texMin[i]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expNQMin.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " delle condizioni di vincolo " }], "Subsection"], Cell["\<\ Notare la tecnica utilizzata per generare la forma TEX di equazioni, \ separando i due mebri.\ \>", "SmallText"], Cell[BoxData[ \(texvincO[i_, j_] := myTeXForm[\(Evaluate[\(eqvinO // Simplify\) // extraSimplify]\)\_\(\(\ \[LeftDoubleBracket]\)\(i, j\)\(\[RightDoubleBracket]\)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texvinc[i_, j_] := myTeXForm[\(Evaluate[\(eqvin // Simplify\) // extraSimplify]\)\_\(\(\ \[LeftDoubleBracket]\)\(i, j\)\(\[RightDoubleBracket]\)\) /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist2}, Do[WriteString[stFile, texvincO[i, 1], "\< &= \>", texvincO[i, 2]]; \[IndentingNewLine]If[i < Length[eqvinO], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]];, {i, 1, Length[eqvinO]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expVincO.tex"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist3}, Do[WriteString[stFile, "\<& \>", texvinc[i, 1], "\< = \>", texvinc[i, 2]]; \[IndentingNewLine]If[i < Length[eqvin], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]];, {i, 1, Length[eqvin]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expVinc.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " delle equazioni di bilancio al bordo" }], "Subsection"], Cell["\<\ Notare la tecnica utilizzata per generare la forma TEX di equazioni, \ separando i due mebri.\ \>", "SmallText"], Cell[BoxData[ \(texeqbdO[i_, j_] := myTeXForm[\(Evaluate[\(eqbilbd /. fabdp // Simplify\) // extraSimplify]\ \)\_\(\(\[LeftDoubleBracket]\)\(i, j\)\(\[RightDoubleBracket]\)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texeqbd[i_, j_] := myTeXForm[\(Evaluate[\(\(eqbilbd /. bulksol\) /. fabdp // Simplify\) // \ extraSimplify]\)\_\(\(\[LeftDoubleBracket]\)\(i, j\)\(\[RightDoubleBracket]\)\ \) /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist1}, Do[WriteString[stFile, texeqbdO[i, 1], "\< &= \>", texeqbdO[i, 2]]; \[IndentingNewLine]If[i < Length[eqbilbd], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]];, {i, 1, Length[eqbilbd]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expBilbdO.tex"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist1}, Do[WriteString[stFile, texeqbd[i, 1], "\< &= \>", texeqbd[i, 2]]; \[IndentingNewLine]If[i < Length[eqbilbd], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]];, {i, 1, Length[eqbilbd]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expBilbd.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " delle costanti di integrazione" }], "Subsection"], Cell[BoxData[ \(texCname[i_] := myTeXForm[\((\(cNQMval\_\(\(\[LeftDoubleBracket]\)\(i, 1\)\(\ \[RightDoubleBracket]\)\) // Simplify\) // extraSimplify)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texCval[i_] := myTeXForm[\((\(\(cNQMval\_\(\(\[LeftDoubleBracket]\)\(i, 2\)\(\ \[RightDoubleBracket]\)\) // Simplify\) // extraSimplify\) // Factor)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texCDval[i_] := myTeXForm[\((\(\(cNQMval\_\(\(\[LeftDoubleBracket]\)\(i, 2\)\(\ \[RightDoubleBracket]\)\) /. cRval // Simplify\) // extraSimplify\) // Factor)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texDname[i_] := myTeXForm[\((\(cRval\_\(\(\[LeftDoubleBracket]\)\(i, 1\)\(\ \[RightDoubleBracket]\)\) // Simplify\) // extraSimplify)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texDval[i_] := myTeXForm[\((\(\(cRval\_\(\(\[LeftDoubleBracket]\)\(i, 2\)\(\ \[RightDoubleBracket]\)\) // Simplify\) // extraSimplify\) // Factor)\) /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist4}, \[IndentingNewLine]Do[ WriteString[stFile, ToString[texCname[i]] <> "\< &= \>", texCval[i]]; \[IndentingNewLine]If[i < Length[cNQMval], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]], {i, 1, Length[cNQMval]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expC.tex"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist5}, \[IndentingNewLine]Do[ WriteString[stFile, ToString[texDname[i]] <> "\< &= \>", texDval[i]]; \[IndentingNewLine]If[i < Length[cRval], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]], {i, 1, Length[cRval]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expD.tex"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist4}, \[IndentingNewLine]Do[ WriteString[stFile, ToString[texCname[i]] <> "\< &= \>", texCDval[i]]; \[IndentingNewLine]If[i < Length[cNQMval], WriteString[stFile, "\< \\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\< \\>.\>"]], {i, 1, Length[cNQMval]}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expCD.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " dei descrittori della tensione (N, Q, M)" }], "Subsection"], Cell[BoxData[ \(texN[i_] := myTeXForm[ Evaluate[\(\(\(\(sN[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texQ[i_] := myTeXForm[ Evaluate[\(\(\(\(sQ[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texM[i_] := myTeXForm[ Evaluate[\(\(\(\(sM[i]\)[\[Zeta]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist1}, Do[\[IndentingNewLine]WriteString[stFile, texNn[i], "\< &= \>", texN[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texQn[i], "\< &= \>", texQ[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texMn[i], "\< &= \>", texM[i]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expNQM.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " degli integrali delle funzioni di risposta senza sostituzioni" }], "Subsection"], Cell["\<\ Prima della sostituzione delle soluzioni delle equazioni di bilancio al bordo\ \ \>", "SmallText"], Cell[BoxData[ \(texu1inO[i_] := \[IndentingNewLine]myTeXForm[ Evaluate[\(\(\(u\_1[i]\)[\[Zeta]] /. vinBer\) /. spsolO // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2inO[i_] := myTeXForm[ Evaluate[\(\(\(u\_2[i]\)[\[Zeta]] /. vinBer\) /. spsolO // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta]inO[i_] := myTeXForm[ Evaluate[\(\(\(\[Theta][i]\)[\[Zeta]] /. vinBer\) /. spsolO // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu1n[i_] := myTeXForm[\(u\_1[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2n[i_] := myTeXForm[\(u\_2[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta]n[i_] := myTeXForm[\(\[Theta][i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist3}, Do[\[IndentingNewLine]WriteString[stFile, texu1n[i], "\< &= \>", texu1inO[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texu2n[i], "\< &= \>", texu2inO[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, tex\[Theta]n[i], "\< &= \>", tex\[Theta]inO[i]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expuvinO.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " degli integrali delle funzioni di risposta" }], "Subsection"], Cell["\<\ Dopo la sostituzione delle soluzioni delle equazioni di bilancio al bordo\ \>", "SmallText"], Cell[BoxData[ \(texu1in[i_] := \[IndentingNewLine]myTeXForm[ Evaluate[\(\(\(u\_1[i]\)[\[Zeta]] /. vinBer\) /. spsol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2in[i_] := myTeXForm[ Evaluate[\(\(\(u\_2[i]\)[\[Zeta]] /. vinBer\) /. spsol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta]in[i_] := myTeXForm[ Evaluate[\(\(\(\[Theta][i]\)[\[Zeta]] /. vinBer\) /. spsol // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu1n[i_] := myTeXForm[\(u\_1[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2n[i_] := myTeXForm[\(u\_2[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta]n[i_] := myTeXForm[\(\[Theta][i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist3}, Do[\[IndentingNewLine]WriteString[stFile, texu1n[i], "\< &= \>", texu1in[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texu2n[i], "\< &= \>", texu2in[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, tex\[Theta]n[i], "\< &= \>", tex\[Theta]in[i]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expuvin.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " degli spostamenti (u, v, \[Theta])" }], "Subsection"], Cell[BoxData[ \(texu1[i_] := myTeXForm[\((\(\(\(\(u\_1[i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2[i_] := myTeXForm[\((\(\(\(\(u\_2[i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify)\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta][i_] := myTeXForm[\((Evaluate[\(\(\(\(\[Theta][i]\)[\[Zeta]] /. vinBer\) /. spsol\) /. cRval // Simplify\) // extraSimplify])\) /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu1n[i_] := myTeXForm[\(u\_1[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texu2n[i_] := myTeXForm[\(u\_2[i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[BoxData[ \(tex\[Theta]n[i_] := myTeXForm[\(\[Theta][i]\)[\[Zeta]] /. newsymlist]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{stFile = OpenWrite["\"]}, Block[{newsymlist = newsymlist2}, \ \[IndentingNewLine]Do[\[IndentingNewLine]WriteString[stFile, texu1n[i], \ "\< &= \>", texu1[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texu2n[i], "\< &= \>", texu2[i]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, tex\[Theta]n[i], "\< &= \>", tex\[Theta][i]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];, {i, 1, travi}]]; \[IndentingNewLine]Close[stFile]]\)], "Input"], Cell[BoxData[ \("expuv.tex"\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Forma ", Cell[BoxData[ StyleBox[ RowBox[{"T", AdjustmentBox["E", BoxMargins->{{-0.075, -0.085}, {0, 0}}, BoxBaselineShift->0.5], "X"}]]]], " delle forze e dei momenti alle estremit\[AGrave]" }], "Subsection"], Cell[BoxData[ \(Clear[texs, texsn]\)], "Input"], Cell[BoxData[ \(texs[i_, meno, j_] := myTeXForm[ Evaluate[\(\(\(\(-\(\(s[i]\)[0]\)\_\(\(\[LeftDoubleBracket]\)\(j\)\(\ \[RightDoubleBracket]\)\)\) /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texs[i_, pi\[UGrave], j_] := myTeXForm[ Evaluate[\(\(\(\(\(s[i]\)[L[i]]\)\_\(\(\[LeftDoubleBracket]\)\(j\)\(\ \[RightDoubleBracket]\)\) /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texm[i_, meno] := myTeXForm[ Evaluate[\(\(\(\(-\(m[i]\)[0]\) /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texm[i_, pi\[UGrave]] := myTeXForm[ Evaluate[\(\(\(\(m[i]\)[L[i]] /. bulksol\) /. cNQMval\) /. cRval // Simplify\) // extraSimplify] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texsn[i_, bd_, j_] := myTeXForm[s\_j[i, bd] /. newsymlist]\)], "Input"], Cell[BoxData[ \(texsm[i_, bd_] := myTeXForm[m[i, bd] /. newsymlist]\)], "Input"], Cell[BoxData[ \(Do[Block[{stFile = OpenWrite["\" <> ToString[i] <> "\<.tex\>"]}, Block[{newsymlist = newsymlist6}, WriteString[stFile, texsn[i, meno, 1], "\< &= \>", texs[i, meno, 1]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texsn[i, meno, 2], "\< &= \>", texs[i, meno, 2]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texsm[i, meno], "\< &= \>", texm[i, meno]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texsn[i, pi\[UGrave], 1], "\< &= \>", texs[i, pi\[UGrave], 1]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texsn[i, pi\[UGrave], 2], "\< &= \>", texs[i, pi\[UGrave], 2]]; WriteString[ stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"]; \ \[IndentingNewLine]WriteString[stFile, texsm[i, pi\[UGrave]], "\< &= \>", texm[i, pi\[UGrave]]]; \[IndentingNewLine]If[i < travi, WriteString[stFile, "\<\\>, \\\>", "\<\[2\jot]\n\>"], WriteString[stFile, "\<\\>.\>"]];]; \[IndentingNewLine]Close[ stFile]], {i, 1, travi}]\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Elenco dei simboli usati", "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[BoxData[ \(TableForm[ Block[{col = 6}, Join[Partition[Names["\"], col], {Take[ Names["\"], \(-\((Length[Names["\"]] - Length[Partition[Names["\"], col] // Flatten])\)\)]}]]]\)], "Input", CellOpen->False], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"a\"\>", "\<\"ambd\"\>", "\<\"ambdv\"\>", "\<\"anyexpr\"\>", "\ \<\"anyexpr$\"\>", "\<\"asseD\"\>"}, {"\<\"asseO\"\>", "\<\"asseOb\"\>", "\<\"b\"\>", "\<\"bd\"\>", \ "\<\"bdj\"\>", "\<\"bi\"\>"}, {"\<\"bix\"\>", "\<\"bj\"\>", "\<\"bjx\"\>", "\<\"bn\"\>", "\<\"bnd\ \"\>", "\<\"bnd1\"\>"}, {"\<\"bnd2\"\>", "\<\"bulksol\"\>", "\<\"bulksolC\"\>", \ "\<\"c\"\>", "\<\"cA\"\>", "\<\"carrello\"\>"}, {"\<\"carrelloFig\"\>", "\<\"carrelloV\"\>", "\<\"cAval\"\>", \ "\<\"cAval0\"\>", "\<\"cAval1\"\>", "\<\"cClist\"\>"}, {"\<\"cDlist\"\>", "\<\"cDlistO\"\>", "\<\"cerniera\"\>", \ "\<\"cernieraFig\"\>", "\<\"cernieraV\"\>", "\<\"cNQM\"\>"}, {"\<\"cNQMb\"\>", "\<\"cNQMsol\"\>", "\<\"cNQMval\"\>", \ "\<\"col\"\>", "\<\"coll\"\>", "\<\"cRlist\"\>"}, {"\<\"cRnull\"\>", "\<\"crosshairFig\"\>", "\<\"cRsol\"\>", \ "\<\"cRsol0\"\>", "\<\"cRsol1\"\>", "\<\"cRval\"\>"}, {"\<\"d\"\>", "\<\"datinum\"\>", "\<\"datiO\"\>", "\<\"datip\"\>", \ "\<\"diaM\"\>", "\<\"diaMb\"\>"}, {"\<\"diaN\"\>", "\<\"diaNb\"\>", "\<\"diaNs\"\>", "\<\"diaQ\"\>", \ "\<\"diaQb\"\>", "\<\"diaQs\"\>"}, {"\<\"dsh\"\>", "\<\"e\"\>", "\<\"eqbil\"\>", "\<\"eqbilbd\"\>", \ "\<\"eqbilt\"\>", "\<\"eqnsp\"\>"}, {"\<\"eqnspO\"\>", "\<\"eqvin\"\>", "\<\"eqvinO\"\>", \ "\<\"exp\"\>", "\<\"expr1\"\>", "\<\"extraSimplify\"\>"}, {"\<\"f\"\>", "\<\"fabd\"\>", "\<\"fabdp\"\>", "\<\"fabdp1\"\>", \ "\<\"fbd\"\>", "\<\"figM\"\>"}, {"\<\"figMb\"\>", "\<\"figN\"\>", "\<\"figNb\"\>", "\<\"figNs\"\>", \ "\<\"figQ\"\>", "\<\"figQb\"\>"}, {"\<\"figQs\"\>", "\<\"forze\"\>", "\<\"frame\"\>", \ "\<\"frameb\"\>", "\<\"fromCtoNQM\"\>", "\<\"fromDtoU\"\>"}, {"\<\"g\"\>", "\<\"grad\"\>", "\<\"grNQM\"\>", \ "\<\"gruv\[Theta]\"\>", "\<\"g$\"\>", "\<\"i\"\>"}, {"\<\"imageH\"\>", "\<\"imageW\"\>", "\<\"incastro\"\>", \ "\<\"incastroFig\"\>", "\<\"incastroV\"\>", "\<\"it\"\>"}, {"\<\"ix\"\>", "\<\"j\"\>", "\<\"jx\"\>", "\<\"ker\"\>", \ "\<\"ker0\"\>", "\<\"L\"\>"}, {"\<\"Li\"\>", "\<\"Lo\"\>", "\<\"m\"\>", "\<\"M\"\>", \ "\<\"matbilbd\"\>", "\<\"matvin\"\>"}, {"\<\"maxL\"\>", "\<\"mb\"\>", "\<\"meno\"\>", "\<\"mU\"\>", \ "\<\"myTeXForm\"\>", "\<\"n\"\>"}, {"\<\"nc\"\>", "\<\"ndiv\"\>", "\<\"newsym\"\>", \ "\<\"newsymlist\"\>", "\<\"newsymlist1\"\>", "\<\"newsymlist2\"\>"}, {"\<\"newsymlist3\"\>", "\<\"newsymlist4\"\>", \ "\<\"newsymlist5\"\>", "\<\"newsymlist6\"\>", "\<\"nf\"\>", "\<\"no\"\>"}, {"\<\"nv\"\>", "\<\"org\"\>", "\<\"outputDir\"\>", "\<\"p\"\>", "\<\ \"perno\"\>", "\<\"pernoFig\"\>"}, {"\<\"pernoV\"\>", "\<\"phframe\"\>", "\<\"pi\[UGrave]\"\>", \ "\<\"pltD\"\>", "\<\"pltDbv\"\>", "\<\"pltDs\"\>"}, {"\<\"pltDv\"\>", "\<\"pltM\"\>", "\<\"pltN\"\>", "\<\"pltO\"\>", "\ \<\"pltOa\"\>", "\<\"pltOax\"\>"}, {"\<\"pltObv\"\>", "\<\"pltOs\"\>", "\<\"pltOv\"\>", \ "\<\"pltOx\"\>", "\<\"pltQ\"\>", "\<\"potbd\"\>"}, {"\<\"potbdv\"\>", "\<\"pote\"\>", "\<\"pt1\"\>", "\<\"pt2\"\>", \ "\<\"rango\"\>", "\<\"risp\"\>"}, {"\<\"s\"\>", "\<\"saldatura\"\>", "\<\"saldaturaFig\"\>", \ "\<\"saldaturaV\"\>", "\<\"sb\"\>", "\<\"sc\"\>"}, {"\<\"scM\"\>", "\<\"scN\"\>", "\<\"scQ\"\>", "\<\"secD\"\>", \ "\<\"secO\"\>", "\<\"simplifyDirac\"\>"}, {"\<\"sM\"\>", "\<\"sMf\"\>", "\<\"sMo\"\>", "\<\"sN\"\>", "\<\"sNf\ \"\>", "\<\"sNo\"\>"}, {"\<\"sNQM\"\>", "\<\"spbd\"\>", "\<\"splist\"\>", \ "\<\"splistV\"\>", "\<\"spro\"\>", "\<\"spsol\"\>"}, {"\<\"spsolD\"\>", "\<\"spsolDO\"\>", "\<\"spsolO\"\>", "\<\"spuv\ \[Theta]\"\>", "\<\"sQ\"\>", "\<\"sQo\"\>"}, {"\<\"stFile\"\>", "\<\"svar\"\>", "\<\"texBil1\"\>", \ "\<\"texBil2\"\>", "\<\"texBil3\"\>", "\<\"texCDval\"\>"}, {"\<\"texCname\"\>", "\<\"texCval\"\>", "\<\"texDname\"\>", \ "\<\"texDval\"\>", "\<\"texeqbd\"\>", "\<\"texeqbdO\"\>"}, {"\<\"texm\"\>", "\<\"texM\"\>", "\<\"texMin\"\>", "\<\"texMn\"\>", \ "\<\"texN\"\>", "\<\"texNin\"\>"}, {"\<\"texNn\"\>", "\<\"texQ\"\>", "\<\"texQin\"\>", \ "\<\"texQn\"\>", "\<\"texs\"\>", "\<\"texsm\"\>"}, {"\<\"texsn\"\>", "\<\"texu1\"\>", "\<\"texu1in\"\>", "\<\"texu1inO\ \"\>", "\<\"texu1n\"\>", "\<\"texu2\"\>"}, {"\<\"texu2in\"\>", "\<\"texu2inO\"\>", "\<\"texu2n\"\>", \ "\<\"texvinc\"\>", "\<\"texvincO\"\>", "\<\"tex\[Theta]\"\>"}, {"\<\"tex\[Theta]in\"\>", "\<\"tex\[Theta]inO\"\>", \ "\<\"tex\[Theta]n\"\>", "\<\"theta\"\>", "\<\"thetao\"\>", "\<\"ticksOption\"\ \>"}, {"\<\"travi\"\>", "\<\"trv\"\>", "\<\"trv1\"\>", "\<\"trv2\"\>", \ "\<\"u\"\>", "\<\"u1\"\>"}, {"\<\"u1o\"\>", "\<\"u2\"\>", "\<\"u2o\"\>", "\<\"ub\"\>", \ "\<\"uo\"\>", "\<\"vam\"\>"}, {"\<\"var\"\>", "\<\"vecOa1\"\>", "\<\"vecOa2\"\>", \ "\<\"vinBer\"\>", "\<\"vincoli\"\>", "\<\"vincolibFig\"\>"}, {"\<\"vincoliDef\"\>", "\<\"vincoliFig\"\>", "\<\"vsp\"\>", "\<\"wb\ \"\>", "\<\"xC\"\>", "\<\"xCshift\"\>"}, {"\<\"xDiag\"\>", "\<\"xLowerL\"\>", "\<\"xMax\"\>", \ "\<\"xMin\"\>", "\<\"xUpperR\"\>", "\<\"y1\"\>"}, {"\<\"y2\"\>", "\<\"YA\"\>", "\<\"YJ\"\>", "\<\"\[ScriptA]\"\>", \ "\<\"\[ScriptB]\"\>", "\<\"\[ScriptC]\"\>"}, {"\<\"\[ScriptCapitalC]\"\>", "\<\"\[ScriptD]\"\>", "\<\"\ \[ScriptCapitalD]\"\>", "\<\"\[ScriptF]\"\>", "\<\"\[ScriptCapitalL]\"\>", \ "\<\"\[ScriptCapitalM]\"\>"}, {"\<\"\[ScriptCapitalY]\[ScriptCapitalA]\"\>", "\<\"\ \[ScriptCapitalY]\[ScriptCapitalJ]\"\>", "\<\"\[Alpha]\"\>", \ "\<\"\[Gamma]\"\>", "\<\"\[Epsilon]\"\>", "\<\"\[Zeta]\"\>"}, {"\<\"\[Zeta]$\"\>", "\<\"\[Theta]\"\>", "\<\"\[Theta]b\"\>", "\<\"\ \[Theta]o\"\>", "\<\"\[Kappa]\"\>", "\<\"\[Xi]\"\>"}, {"\<\"\[Chi]\"\>", "\<\"\[Omega]b\"\>", "\<\"\"\>", "\<\"\"\>", "\<\ \"\"\>", "\<\"\"\>"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], TableForm[ {{"a", "ambd", "ambdv", "anyexpr", "anyexpr$", "asseD"}, { "asseO", "asseOb", "b", "bd", "bdj", "bi"}, {"bix", "bj", "bjx", "bn", "bnd", "bnd1"}, {"bnd2", "bulksol", "bulksolC", "c", "cA", "carrello"}, {"carrelloFig", "carrelloV", "cAval", "cAval0", "cAval1", "cClist"}, {"cDlist", "cDlistO", "cerniera", "cernieraFig", "cernieraV", "cNQM"}, {"cNQMb", "cNQMsol", "cNQMval", "col", "coll", "cRlist"}, {"cRnull", "crosshairFig", "cRsol", "cRsol0", "cRsol1", "cRval"}, {"d", "datinum", "datiO", "datip", "diaM", "diaMb"}, { "diaN", "diaNb", "diaNs", "diaQ", "diaQb", "diaQs"}, {"dsh", "e", "eqbil", "eqbilbd", "eqbilt", "eqnsp"}, {"eqnspO", "eqvin", "eqvinO", "exp", "expr1", "extraSimplify"}, {"f", "fabd", "fabdp", "fabdp1", "fbd", "figM"}, {"figMb", "figN", "figNb", "figNs", "figQ", "figQb"}, {"figQs", "forze", "frame", "frameb", "fromCtoNQM", "fromDtoU"}, {"g", "grad", "grNQM", "gruv\[Theta]", "g$", "i"}, { "imageH", "imageW", "incastro", "incastroFig", "incastroV", "it"}, { "ix", "j", "jx", "ker", "ker0", "L"}, {"Li", "Lo", "m", "M", "matbilbd", "matvin"}, {"maxL", "mb", "meno", "mU", "myTeXForm", "n"}, {"nc", "ndiv", "newsym", "newsymlist", "newsymlist1", "newsymlist2"}, {"newsymlist3", "newsymlist4", "newsymlist5", "newsymlist6", "nf", "no"}, {"nv", "org", "outputDir", "p", "perno", "pernoFig"}, {"pernoV", "phframe", "pi\[UGrave]", "pltD", "pltDbv", "pltDs"}, {"pltDv", "pltM", "pltN", "pltO", "pltOa", "pltOax"}, { "pltObv", "pltOs", "pltOv", "pltOx", "pltQ", "potbd"}, {"potbdv", "pote", "pt1", "pt2", "rango", "risp"}, {"s", "saldatura", "saldaturaFig", "saldaturaV", "sb", "sc"}, {"scM", "scN", "scQ", "secD", "secO", "simplifyDirac"}, {"sM", "sMf", "sMo", "sN", "sNf", "sNo"}, {"sNQM", "spbd", "splist", "splistV", "spro", "spsol"}, { "spsolD", "spsolDO", "spsolO", "spuv\[Theta]", "sQ", "sQo"}, { "stFile", "svar", "texBil1", "texBil2", "texBil3", "texCDval"}, { "texCname", "texCval", "texDname", "texDval", "texeqbd", "texeqbdO"}, {"texm", "texM", "texMin", "texMn", "texN", "texNin"}, { "texNn", "texQ", "texQin", "texQn", "texs", "texsm"}, {"texsn", "texu1", "texu1in", "texu1inO", "texu1n", "texu2"}, {"texu2in", "texu2inO", "texu2n", "texvinc", "texvincO", "tex\[Theta]"}, { "tex\[Theta]in", "tex\[Theta]inO", "tex\[Theta]n", "theta", "thetao", "ticksOption"}, {"travi", "trv", "trv1", "trv2", "u", "u1"}, {"u1o", "u2", "u2o", "ub", "uo", "vam"}, {"var", "vecOa1", "vecOa2", "vinBer", "vincoli", "vincolibFig"}, {"vincoliDef", "vincoliFig", "vsp", "wb", "xC", "xCshift"}, {"xDiag", "xLowerL", "xMax", "xMin", "xUpperR", "y1"}, {"y2", "YA", "YJ", "\[ScriptA]", "\[ScriptB]", "\[ScriptC]"}, { "\[ScriptCapitalC]", "\[ScriptD]", "\[ScriptCapitalD]", "\[ScriptF]", "\[ScriptCapitalL]", "\[ScriptCapitalM]"}, { "\[ScriptCapitalY]\[ScriptCapitalA]", "\[ScriptCapitalY]\[ScriptCapitalJ]", "\[Alpha]", "\[Gamma]", "\[Epsilon]", "\[Zeta]"}, {"\[Zeta]$", "\[Theta]", "\[Theta]b", "\[Theta]o", "\[Kappa]", "\[Xi]"}, {"\[Chi]", "\[Omega]b"}}]]], "Output"] }, Open ]] }, Closed]] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{605, 668}, WindowMargins->{{Automatic, 0}, {Automatic, 0}}, Magnification->1 ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1727, 52, 98, 3, 280, "Title"], Cell[1828, 57, 308, 9, 85, "Subtitle", Evaluatable->False], Cell[2139, 68, 358, 9, 105, "Subtitle", Evaluatable->False], Cell[CellGroupData[{ Cell[2522, 81, 51, 1, 59, "Section", Evaluatable->False], Cell[2576, 84, 1127, 30, 252, "SmallText"], Cell[3706, 116, 1520, 27, 236, "SmallText"], Cell[5229, 145, 498, 12, 60, "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell[5764, 162, 57, 1, 39, "Section", Evaluatable->False], Cell[5824, 165, 107, 2, 50, "Input"], Cell[CellGroupData[{ Cell[5956, 171, 56, 1, 30, "Input"], Cell[6015, 174, 92, 1, 29, "Output"] }, Open ]], Cell[6122, 178, 97, 2, 28, "SmallText"], Cell[6222, 182, 130, 2, 50, "Input"], Cell[6355, 186, 495, 8, 150, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[6887, 199, 161, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[7073, 209, 84, 2, 47, "Subsection"], Cell[7160, 213, 109, 2, 28, "SmallText"], Cell[7272, 217, 128, 4, 50, "Input"], Cell[7403, 223, 131, 4, 28, "SmallText"], Cell[7537, 229, 245, 6, 50, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[7819, 240, 103, 5, 31, "Subsection"], Cell[7925, 247, 46, 0, 28, "SmallText"], Cell[7974, 249, 101, 3, 46, "Input"], Cell[8078, 254, 364, 10, 60, "SmallText"], Cell[8445, 266, 121, 3, 56, "Input"], Cell[8569, 271, 319, 9, 60, "SmallText"], Cell[8891, 282, 116, 3, 46, "Input"], Cell[9010, 287, 215, 5, 66, "Input"], Cell[9228, 294, 130, 3, 28, "SmallText"], Cell[9361, 299, 129, 3, 46, "Input"], Cell[9493, 304, 121, 3, 28, "SmallText"], Cell[9617, 309, 199, 5, 58, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[9853, 319, 56, 0, 31, "Subsection"], Cell[9912, 321, 45, 0, 28, "SmallText"], Cell[9960, 323, 124, 3, 30, "Input"], Cell[10087, 328, 42, 0, 28, "SmallText"], Cell[10132, 330, 118, 2, 30, "Input"], Cell[10253, 334, 43, 1, 30, "Input"], Cell[10299, 337, 227, 4, 28, "SmallText"], Cell[10529, 343, 53, 1, 30, "Input"], Cell[10585, 346, 271, 5, 42, "Input"], Cell[10859, 353, 46, 0, 28, "SmallText"], Cell[10908, 355, 195, 4, 42, "Input"], Cell[11106, 361, 52, 0, 28, "SmallText"], Cell[11161, 363, 504, 9, 131, "Input"], Cell[11668, 374, 613, 11, 131, "Input"], Cell[12284, 387, 73, 0, 28, "SmallText"], Cell[12360, 389, 46, 1, 30, "Input"], Cell[12409, 392, 134, 3, 28, "SmallText"], Cell[12546, 397, 182, 4, 30, "Input"], Cell[12731, 403, 146, 3, 30, "Input"], Cell[12880, 408, 42, 0, 28, "SmallText"], Cell[12925, 410, 203, 4, 42, "Input"], Cell[13131, 416, 48, 0, 28, "SmallText"], Cell[13182, 418, 226, 5, 85, "Input"], Cell[13411, 425, 205, 5, 42, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[13653, 435, 111, 3, 50, "Subsection"], Cell[CellGroupData[{ Cell[13789, 442, 144, 2, 70, "Input"], Cell[13936, 446, 7780, 161, 296, 953, 72, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[21777, 614, 150, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[21952, 624, 103, 5, 47, "Subsection"], Cell[22058, 631, 62, 1, 30, "Input"], Cell[22123, 634, 57, 1, 30, "Input"], Cell[22183, 637, 417, 11, 76, "SmallText"], Cell[22603, 650, 130, 3, 46, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[22770, 658, 210, 7, 66, "Subsection"], Cell[CellGroupData[{ Cell[23005, 669, 52, 1, 30, "Input"], Cell[23060, 672, 46, 1, 70, "Output"] }, Open ]], Cell[23121, 676, 310, 5, 116, "Input"], Cell[CellGroupData[{ Cell[23456, 685, 50, 1, 30, "Input"], Cell[23509, 688, 46, 1, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[23616, 696, 116, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[23757, 703, 132, 3, 47, "Subsection"], Cell[23892, 708, 137, 3, 30, "Input"], Cell[24032, 713, 74, 1, 30, "Input"], Cell[24109, 716, 1102, 28, 50, "Input"], Cell[CellGroupData[{ Cell[25236, 748, 92, 1, 30, "Input"], Cell[25331, 751, 55, 1, 70, "Output"] }, Open ]], Cell[25401, 755, 105, 2, 30, "Input"], Cell[CellGroupData[{ Cell[25531, 761, 174, 3, 30, "Input"], Cell[25708, 766, 405, 9, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[26162, 781, 64, 0, 31, "Subsection"], Cell[26229, 783, 280, 6, 44, "SmallText"], Cell[CellGroupData[{ Cell[26534, 793, 87, 1, 30, "Input"], Cell[26624, 796, 109, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26770, 803, 104, 2, 30, "Input"], Cell[26877, 807, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26972, 813, 190, 3, 50, "Input"], Cell[27165, 818, 139, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27341, 825, 264, 4, 71, "Input"], Cell[27608, 831, 154, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27799, 838, 65, 1, 30, "Input"], Cell[27867, 841, 345, 7, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[28261, 854, 66, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[28352, 858, 116, 2, 30, "Input"], Cell[28471, 862, 1504, 46, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[30012, 913, 290, 5, 50, "Input"], Cell[30305, 920, 1325, 39, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[31667, 964, 289, 5, 50, "Input"], Cell[31959, 971, 1186, 37, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[33206, 1015, 62, 0, 39, "Section"], Cell[33271, 1017, 71, 1, 30, "Input"], Cell[33345, 1020, 146, 3, 28, "SmallText"], Cell[33494, 1025, 408, 9, 70, "Input"], Cell[33905, 1036, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[34000, 1040, 198, 4, 30, "Input"], Cell[34201, 1046, 174, 3, 70, "Output"] }, Open ]], Cell[34390, 1052, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[34485, 1056, 198, 4, 30, "Input"], Cell[34686, 1062, 174, 3, 70, "Output"] }, Open ]], Cell[34875, 1068, 64, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[34964, 1072, 190, 4, 30, "Input"], Cell[35157, 1078, 151, 2, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[35357, 1086, 128, 5, 39, "Section"], Cell[CellGroupData[{ Cell[35510, 1095, 53, 0, 47, "Subsection"], Cell[35566, 1097, 110, 2, 30, "Input"], Cell[35679, 1101, 152, 3, 30, "Input"], Cell[35834, 1106, 249, 5, 50, "Input"], Cell[36086, 1113, 330, 6, 70, "Input"], Cell[36419, 1121, 193, 4, 30, "Input"], Cell[36615, 1127, 133, 3, 28, "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell[36785, 1135, 103, 5, 31, "Subsection"], Cell[36891, 1142, 160, 4, 60, "SmallText"], Cell[37054, 1148, 49, 1, 30, "Input"], Cell[37106, 1151, 106, 2, 50, "Input"], Cell[37215, 1155, 119, 3, 28, "SmallText"], Cell[37337, 1160, 185, 4, 66, "Input"], Cell[37525, 1166, 505, 8, 92, "SmallText"], Cell[38033, 1176, 165, 4, 46, "Input"], Cell[38201, 1182, 224, 3, 110, "Input"], Cell[CellGroupData[{ Cell[38450, 1189, 40, 1, 30, "Input"], Cell[38493, 1192, 210, 3, 85, "Output"] }, Open ]], Cell[38718, 1198, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[38813, 1202, 137, 3, 30, "Input"], Cell[38953, 1207, 172, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[39174, 1216, 56, 0, 31, "Subsection"], Cell[39233, 1218, 72, 0, 28, "SmallText"], Cell[39308, 1220, 44, 1, 30, "Input"], Cell[CellGroupData[{ Cell[39377, 1225, 43, 1, 30, "Input"], Cell[39423, 1228, 78, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39538, 1234, 280, 5, 90, "Input"], Cell[39821, 1241, 36, 1, 70, "Output"] }, Open ]], Cell[39872, 1245, 150, 3, 44, "SmallText"], Cell[40025, 1250, 43, 1, 30, "Input"], Cell[40071, 1253, 53, 1, 30, "Input"], Cell[40127, 1256, 1277, 26, 270, "Input"], Cell[CellGroupData[{ Cell[41429, 1286, 240, 4, 70, "Input"], Cell[41672, 1292, 36, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41745, 1298, 48, 1, 30, "Input"], Cell[41796, 1301, 396, 12, 70, "Output"] }, Open ]], Cell[42207, 1316, 90, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[42322, 1322, 43, 1, 30, "Input"], Cell[42368, 1325, 78, 1, 70, "Output"] }, Open ]], Cell[42461, 1329, 222, 4, 90, "Input"], Cell[42686, 1335, 219, 4, 90, "Input"], Cell[42908, 1341, 67, 0, 28, "SmallText"], Cell[42978, 1343, 72, 1, 30, "Input"], Cell[43053, 1346, 82, 1, 30, "Input"], Cell[43138, 1349, 393, 7, 208, "Input"], Cell[43534, 1358, 403, 7, 208, "Input"], Cell[43940, 1367, 214, 4, 118, "Input"], Cell[44157, 1373, 717, 13, 338, "Input"], Cell[44877, 1388, 452, 8, 202, "Input"], Cell[45332, 1398, 213, 4, 90, "Input"], Cell[45548, 1404, 155, 3, 70, "Input"], Cell[45706, 1409, 57, 1, 30, "Input"], Cell[45766, 1412, 59, 1, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[45862, 1418, 75, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[45962, 1422, 145, 2, 70, "Input"], Cell[46110, 1426, 9874, 194, 324, 1099, 81, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[56021, 1625, 144, 2, 70, "Input"], Cell[56168, 1629, 7214, 161, 303, 1104, 81, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[63431, 1796, 78, 0, 47, "Subsection"], Cell[63512, 1798, 231, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[63768, 1806, 213, 4, 50, "Input"], Cell[63984, 1812, 886, 28, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[64907, 1845, 70, 1, 30, "Input"], Cell[64980, 1848, 961, 29, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[66002, 1884, 89, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[66116, 1889, 68, 1, 47, "Subsection", Evaluatable->False], Cell[66187, 1892, 119, 3, 28, "SmallText"], Cell[66309, 1897, 156, 3, 28, "SmallText"], Cell[66468, 1902, 356, 5, 95, "Input"], Cell[66827, 1909, 343, 6, 115, "Input"], Cell[CellGroupData[{ Cell[67195, 1919, 37, 1, 30, "Input"], Cell[67235, 1922, 311, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[67583, 1932, 71, 1, 30, "Input"], Cell[67657, 1935, 753, 13, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[68459, 1954, 57, 0, 31, "Subsection"], Cell[68519, 1956, 94, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[68638, 1962, 169, 3, 30, "Input"], Cell[68810, 1967, 212, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[69059, 1975, 93, 1, 30, "Input"], Cell[69155, 1978, 210, 3, 70, "Output"] }, Open ]], Cell[69380, 1984, 61, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[69466, 1988, 344, 6, 90, "Input"], Cell[69813, 1996, 172, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[70022, 2004, 69, 1, 30, "Input"], Cell[70094, 2007, 76, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[70219, 2014, 65, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[70309, 2018, 70, 1, 30, "Input"], Cell[70382, 2021, 203, 3, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[70634, 2030, 105, 2, 50, "Subsection"], Cell[CellGroupData[{ Cell[70764, 2036, 195, 4, 30, "Input"], Cell[70962, 2042, 152, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[71151, 2050, 63, 1, 30, "Input"], Cell[71217, 2053, 124, 2, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[71390, 2061, 88, 1, 31, "Subsection", Evaluatable->False], Cell[71481, 2064, 180, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[71686, 2072, 37, 1, 30, "Input"], Cell[71726, 2075, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[71821, 2081, 138, 4, 30, "Input"], Cell[71962, 2087, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[72057, 2093, 103, 2, 30, "Input"], Cell[72163, 2097, 148, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[72348, 2105, 134, 3, 30, "Input"], Cell[72485, 2110, 256, 7, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[72778, 2122, 134, 3, 30, "Input"], Cell[72915, 2127, 366, 12, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[73330, 2145, 78, 0, 31, "Subsection"], Cell[73411, 2147, 83, 1, 28, "SmallText"], Cell[CellGroupData[{ Cell[73519, 2152, 45, 1, 30, "Input"], Cell[73567, 2155, 35, 1, 70, "Output"] }, Open ]], Cell[73617, 2159, 218, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[73860, 2167, 51, 1, 30, "Input"], Cell[73914, 2170, 35, 1, 70, "Output"] }, Open ]], Cell[73964, 2174, 123, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[74112, 2181, 53, 1, 30, "Input"], Cell[74168, 2184, 35, 1, 70, "Output"] }, Open ]], Cell[74218, 2188, 132, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[74375, 2195, 51, 1, 30, "Input"], Cell[74429, 2198, 35, 1, 70, "Output"] }, Open ]], Cell[74479, 2202, 30, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[74534, 2206, 134, 2, 30, "Input"], Cell[74671, 2210, 52, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[74760, 2216, 230, 5, 30, "Input"], Cell[74993, 2223, 35, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[75077, 2230, 72, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[75174, 2234, 461, 8, 19, "Input", CellOpen->False], Cell[75638, 2244, 195, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[75870, 2254, 1993, 32, 19, "Input", CellOpen->False], Cell[77866, 2288, 189, 5, 70, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[78116, 2300, 142, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[78283, 2310, 56, 0, 47, "Subsection"], Cell[78342, 2312, 75, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[78442, 2316, 92, 1, 50, "Input"], Cell[78537, 2319, 121, 2, 70, "Output"] }, Open ]], Cell[78673, 2324, 182, 3, 44, "SmallText"], Cell[78858, 2329, 248, 7, 50, "Input"], Cell[CellGroupData[{ Cell[79131, 2340, 71, 1, 30, "Input"], Cell[79205, 2343, 318, 10, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[79572, 2359, 134, 5, 31, "Subsection"], Cell[79709, 2366, 420, 7, 76, "SmallText"], Cell[80132, 2375, 104, 3, 46, "Input"], Cell[80239, 2380, 313, 9, 44, "SmallText"], Cell[80555, 2391, 407, 8, 106, "Input"], Cell[80965, 2401, 90, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[81080, 2407, 135, 3, 30, "Input"], Cell[81218, 2412, 36, 1, 70, "Output"] }, Open ]], Cell[81269, 2416, 127, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[81421, 2423, 140, 3, 70, "Input"], Cell[81564, 2428, 69, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[81670, 2434, 182, 4, 50, "Input"], Cell[81855, 2440, 89, 1, 70, "Output"] }, Open ]], Cell[81959, 2444, 46, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[82030, 2448, 46, 1, 30, "Input"], Cell[82079, 2451, 40, 1, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[82168, 2458, 72, 0, 31, "Subsection"], Cell[82243, 2460, 141, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[82409, 2467, 271, 7, 50, "Input"], Cell[82683, 2476, 42, 1, 70, "Output"] }, Open ]], Cell[82740, 2480, 185, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[82950, 2488, 160, 4, 30, "Input"], Cell[83113, 2494, 36, 1, 70, "Output"] }, Open ]], Cell[83164, 2498, 524, 9, 110, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[83737, 2513, 88, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[83850, 2518, 52, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[83927, 2522, 76, 1, 30, "Input"], Cell[84006, 2525, 78, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[84133, 2532, 91, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[84249, 2537, 571, 10, 70, "Input"], Cell[84823, 2549, 75, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84935, 2555, 149, 2, 30, "Input"], Cell[85087, 2559, 232, 4, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[85356, 2568, 40, 1, 30, "Input"], Cell[85399, 2571, 75, 1, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[85535, 2579, 116, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[85676, 2586, 45, 0, 47, "Subsection"], Cell[85724, 2588, 141, 3, 30, "Input"], Cell[CellGroupData[{ Cell[85890, 2595, 1094, 25, 50, "Input"], Cell[86987, 2622, 1015, 24, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[88051, 2652, 65, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[88141, 2656, 217, 4, 50, "Input"], Cell[88361, 2662, 186, 3, 70, "Output"] }, Open ]], Cell[88562, 2668, 79, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[88666, 2672, 365, 9, 30, "Input"], Cell[89034, 2683, 320, 8, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[89403, 2697, 40, 0, 31, "Subsection"], Cell[89446, 2699, 142, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[89613, 2706, 227, 3, 50, "Input"], Cell[89843, 2711, 366, 7, 70, "Output"] }, Open ]], Cell[90224, 2721, 108, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[90357, 2728, 289, 4, 70, "Input"], Cell[90649, 2734, 822, 17, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91508, 2756, 246, 4, 70, "Input"], Cell[91757, 2762, 595, 10, 70, "Output"] }, Open ]], Cell[92367, 2775, 102, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[92494, 2781, 330, 5, 70, "Input"], Cell[92827, 2788, 788, 17, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93652, 2810, 244, 4, 70, "Input"], Cell[93899, 2816, 550, 9, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94486, 2830, 169, 3, 30, "Input"], Cell[94658, 2835, 115, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94810, 2842, 76, 1, 30, "Input"], Cell[94889, 2845, 693, 11, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[95619, 2861, 75, 1, 30, "Input"], Cell[95697, 2864, 630, 11, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[96376, 2881, 64, 0, 31, "Subsection"], Cell[96443, 2883, 225, 5, 44, "SmallText"], Cell[CellGroupData[{ Cell[96693, 2892, 190, 4, 50, "Input"], Cell[96886, 2898, 109, 2, 70, "Output"] }, Open ]], Cell[97010, 2903, 112, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[97147, 2910, 311, 7, 90, "Input"], Cell[97461, 2919, 117, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[97615, 2926, 257, 4, 50, "Input"], Cell[97875, 2932, 149, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[98061, 2939, 127, 2, 31, "Input"], Cell[98191, 2943, 164, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[98392, 2950, 60, 1, 30, "Input"], Cell[98455, 2953, 76, 1, 70, "Output"] }, Open ]], Cell[98546, 2957, 108, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[98679, 2964, 61, 1, 30, "Input"], Cell[98743, 2967, 574, 10, 70, "Output"] }, Open ]], Cell[99332, 2980, 102, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[99459, 2986, 59, 1, 30, "Input"], Cell[99521, 2989, 529, 9, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[100111, 3005, 78, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[100214, 3010, 64, 1, 47, "Subsection", Evaluatable->False], Cell[100281, 3013, 151, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[100457, 3020, 422, 8, 90, "Input"], Cell[100882, 3030, 214, 3, 70, "Output"] }, Open ]], Cell[101111, 3036, 191, 4, 28, "SmallText"], Cell[CellGroupData[{ Cell[101327, 3044, 82, 1, 30, "Input"], Cell[101412, 3047, 651, 11, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[102112, 3064, 78, 1, 31, "Subsection", Evaluatable->False], Cell[102193, 3067, 108, 2, 30, "Input"], Cell[CellGroupData[{ Cell[102326, 3073, 93, 1, 30, "Input"], Cell[102422, 3076, 560, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[103019, 3093, 93, 1, 30, "Input"], Cell[103115, 3096, 1186, 31, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[104338, 3132, 107, 2, 30, "Input"], Cell[104448, 3136, 35, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[104520, 3142, 108, 2, 30, "Input"], Cell[104631, 3146, 36, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[104704, 3152, 39, 1, 30, "Input"], Cell[104746, 3155, 76, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[104871, 3162, 55, 0, 31, "Subsection"], Cell[104929, 3164, 246, 4, 110, "Input"], Cell[105178, 3170, 244, 4, 110, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[105459, 3179, 80, 1, 47, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[105564, 3184, 169, 3, 30, "Input"], Cell[105736, 3189, 586, 8, 70, "Output"] }, Open ]], Cell[106337, 3200, 42, 1, 30, "Input"], Cell[106382, 3203, 86, 1, 30, "Input"], Cell[CellGroupData[{ Cell[106493, 3208, 88, 1, 30, "Input"], Cell[106584, 3211, 586, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[107207, 3224, 221, 4, 30, "Input"], Cell[107431, 3230, 752, 13, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[108220, 3248, 128, 2, 30, "Input"], Cell[108351, 3252, 3024, 75, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[111436, 3334, 123, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[111584, 3341, 140, 5, 47, "Subsection"], Cell[111727, 3348, 110, 2, 30, "Input"], Cell[111840, 3352, 78, 1, 30, "Input"], Cell[111921, 3355, 76, 1, 30, "Input"], Cell[112000, 3358, 59, 1, 30, "Input"], Cell[112062, 3361, 471, 8, 139, "Input"], Cell[112536, 3371, 65, 1, 30, "Input"], Cell[112604, 3374, 85, 1, 30, "Input"], Cell[112692, 3377, 150, 3, 70, "Input"], Cell[112845, 3382, 193, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[113063, 3390, 304, 5, 130, "Input"], Cell[113370, 3397, 38, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[113457, 3404, 64, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[113546, 3408, 91, 1, 30, "Input"], Cell[113640, 3411, 75, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[113752, 3417, 89, 1, 30, "Input"], Cell[113844, 3420, 648, 11, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[114541, 3437, 36, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[114602, 3441, 38, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[114665, 3445, 297, 6, 90, "Input"], Cell[114965, 3453, 483, 12, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[115497, 3471, 40, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[115562, 3475, 292, 6, 90, "Input"], Cell[115857, 3483, 483, 12, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[116389, 3501, 32, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[116446, 3505, 292, 6, 90, "Input"], Cell[116741, 3513, 520, 13, 70, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[117322, 3533, 33, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[117380, 3537, 44, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[117449, 3541, 289, 6, 130, "Input"], Cell[117741, 3549, 658, 15, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[118448, 3570, 48, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[118521, 3574, 289, 6, 130, "Input"], Cell[118813, 3582, 715, 17, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[119577, 3605, 34, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[119636, 3609, 295, 6, 130, "Input"], Cell[119934, 3617, 730, 16, 70, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[120725, 3640, 118, 3, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[120868, 3647, 58, 1, 30, "Input"], Cell[120929, 3650, 411, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[121377, 3667, 62, 0, 43, "Subsubsection"], Cell[121442, 3669, 59, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[121526, 3673, 302, 5, 150, "Input"], Cell[121831, 3680, 507, 12, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[122387, 3698, 64, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[122476, 3702, 302, 5, 150, "Input"], Cell[122781, 3709, 437, 12, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[123267, 3727, 52, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[123344, 3731, 453, 8, 189, "Input"], Cell[123800, 3741, 337, 10, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[124186, 3757, 54, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[124265, 3761, 623, 11, 191, "Input"], Cell[124891, 3774, 330, 10, 70, "Output"] }, Open ]] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[125294, 3792, 131, 6, 39, "Section", Evaluatable->False], Cell[125428, 3800, 118, 3, 33, "Text"], Cell[125549, 3805, 219, 5, 46, "Input"], Cell[125771, 3812, 225, 4, 71, "Text"], Cell[CellGroupData[{ Cell[126021, 3820, 132, 3, 50, "Input"], Cell[126156, 3825, 36, 1, 70, "Output"] }, Open ]], Cell[126207, 3829, 123, 3, 33, "Text"], Cell[126333, 3834, 102, 3, 46, "Input"], Cell[CellGroupData[{ Cell[126460, 3841, 142, 3, 70, "Input"], Cell[126605, 3846, 36, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[126678, 3852, 69, 1, 30, "Input"], Cell[126750, 3855, 175, 3, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[126974, 3864, 107, 3, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[127106, 3871, 33, 0, 47, "Subsection"], Cell[127142, 3873, 215, 4, 50, "Input"], Cell[127360, 3879, 214, 4, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[127611, 3888, 66, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[127702, 3893, 67, 1, 30, "Input"], Cell[127772, 3896, 546, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[128355, 3909, 68, 1, 30, "Input"], Cell[128426, 3912, 43, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[128506, 3918, 81, 1, 30, "Input"], Cell[128590, 3921, 238, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[128865, 3931, 84, 1, 30, "Input"], Cell[128952, 3934, 249, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[129238, 3944, 73, 1, 30, "Input"], Cell[129314, 3947, 233, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[129584, 3955, 76, 1, 30, "Input"], Cell[129663, 3958, 374, 6, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[130074, 3969, 73, 1, 30, "Input"], Cell[130150, 3972, 76, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[130263, 3978, 76, 1, 30, "Input"], Cell[130342, 3981, 85, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[130476, 3988, 75, 1, 31, "Subsection", Evaluatable->False], Cell[130554, 3991, 384, 16, 28, "SmallText"], Cell[130941, 4009, 261, 12, 28, "SmallText"], Cell[131205, 4023, 1652, 33, 152, "Input"], Cell[132860, 4058, 1634, 32, 152, "Input"], Cell[134497, 4092, 393, 16, 50, "Text"], Cell[134893, 4110, 64, 1, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[134994, 4116, 92, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[135111, 4121, 132, 3, 19, "Input", CellOpen->False], Cell[135246, 4126, 11867, 427, 77, 5164, 341, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[147162, 4559, 94, 3, 47, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[147281, 4566, 155, 4, 19, "Input", CellOpen->False], Cell[147439, 4572, 14300, 528, 81, 6558, 430, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[161800, 5107, 165, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[161990, 5117, 56, 0, 47, "Subsection"], Cell[162049, 5119, 136, 3, 28, "SmallText"], Cell[162188, 5124, 222, 5, 30, "Input"], Cell[162413, 5131, 446, 7, 84, "Input"], Cell[162862, 5140, 38, 0, 28, "SmallText"], Cell[162903, 5142, 328, 7, 50, "Input"], Cell[163234, 5151, 42, 0, 28, "SmallText"], Cell[163279, 5153, 229, 5, 63, "Input"], Cell[CellGroupData[{ Cell[163533, 5162, 86, 1, 30, "Input"], Cell[163622, 5165, 308, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[163967, 5178, 88, 1, 30, "Input"], Cell[164058, 5181, 308, 8, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[164415, 5195, 42, 0, 31, "Subsection"], Cell[164460, 5197, 232, 4, 28, "SmallText"], Cell[CellGroupData[{ Cell[164717, 5205, 263, 5, 90, "Input"], Cell[164983, 5212, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[165064, 5218, 263, 5, 90, "Input"], Cell[165330, 5225, 86, 1, 70, "Output"] }, Open ]], Cell[165431, 5229, 86, 1, 30, "Input"], Cell[165520, 5232, 128, 2, 76, "Input"], Cell[165651, 5236, 112, 2, 30, "Input"], Cell[165766, 5240, 129, 3, 30, "Input"], Cell[165898, 5245, 67, 1, 42, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[166002, 5251, 132, 5, 31, "Subsection"], Cell[166137, 5258, 181, 5, 44, "SmallText"], Cell[CellGroupData[{ Cell[166343, 5267, 83, 1, 32, "Input"], Cell[166429, 5270, 60, 1, 29, "Output"] }, Open ]], Cell[166504, 5274, 182, 6, 41, "Input"], Cell[CellGroupData[{ Cell[166711, 5284, 62, 1, 30, "Input"], Cell[166776, 5287, 143, 3, 29, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[166968, 5296, 28, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[167021, 5300, 221, 3, 70, "Input"], Cell[167245, 5305, 17944, 357, 297, 2082, 157, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[185226, 5667, 219, 3, 70, "Input"], Cell[185448, 5672, 14887, 322, 296, 2074, 159, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[200396, 6001, 159, 6, 59, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[200580, 6011, 34, 0, 47, "Subsection"], Cell[200617, 6013, 136, 3, 28, "SmallText"], Cell[200756, 6018, 191, 4, 30, "Input"], Cell[200950, 6024, 36, 0, 28, "SmallText"], Cell[200989, 6026, 349, 8, 50, "Input"], Cell[201341, 6036, 46, 0, 28, "SmallText"], Cell[201390, 6038, 925, 20, 210, "Input"], Cell[202318, 6060, 122, 3, 30, "Input"], Cell[202443, 6065, 109, 2, 50, "Input"], Cell[202555, 6069, 109, 2, 50, "Input"], Cell[202667, 6073, 270, 5, 70, "Input"], Cell[202940, 6080, 191, 4, 30, "Input"], Cell[203134, 6086, 349, 8, 50, "Input"], Cell[203486, 6096, 925, 20, 210, "Input"], Cell[204414, 6118, 122, 3, 30, "Input"], Cell[204539, 6123, 109, 2, 50, "Input"], Cell[204651, 6127, 109, 2, 50, "Input"], Cell[204763, 6131, 270, 5, 70, "Input"], Cell[205036, 6138, 191, 4, 30, "Input"], Cell[205230, 6144, 349, 8, 50, "Input"], Cell[205582, 6154, 122, 3, 30, "Input"], Cell[205707, 6159, 109, 2, 50, "Input"], Cell[205819, 6163, 263, 5, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[206119, 6173, 128, 5, 31, "Subsection"], Cell[206250, 6180, 48, 1, 30, "Input"], Cell[206301, 6183, 49, 1, 30, "Input"], Cell[206353, 6186, 48, 1, 30, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[206438, 6192, 51, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[206514, 6196, 167, 2, 70, "Input"], Cell[206684, 6200, 11934, 320, 296, 3086, 206, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[218667, 6526, 42, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[218734, 6530, 167, 2, 70, "Input"], Cell[218904, 6534, 14251, 348, 296, 3091, 206, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[233204, 6888, 43, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[233272, 6892, 167, 2, 70, "Input"], Cell[233442, 6896, 11722, 278, 296, 2429, 159, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[245225, 7181, 104, 1, 59, "Section"], Cell[CellGroupData[{ Cell[245354, 7186, 44, 1, 30, "Input"], Cell[245401, 7189, 92, 1, 70, "Output"] }, Open ]], Cell[245508, 7193, 137, 3, 70, "Input"], Cell[245648, 7198, 231, 4, 70, "Input"], Cell[245882, 7204, 237, 4, 70, "Input"], Cell[246122, 7210, 114, 2, 44, "SmallText"], Cell[CellGroupData[{ Cell[246261, 7216, 328, 5, 72, "Input"], Cell[246592, 7223, 42, 1, 70, "Output"] }, Open ]], Cell[246649, 7227, 255, 4, 90, "Input"], Cell[246907, 7233, 257, 4, 90, "Input"], Cell[247167, 7239, 281, 5, 90, "Input"], Cell[247451, 7246, 254, 4, 90, "Input"], Cell[247708, 7252, 254, 4, 90, "Input"], Cell[247965, 7258, 254, 4, 90, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[248256, 7267, 301, 10, 39, "Section"], Cell[CellGroupData[{ Cell[248582, 7281, 42, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[248649, 7285, 44, 1, 30, "Input"], Cell[248696, 7288, 92, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[248825, 7294, 69, 1, 30, "Input"], Cell[248897, 7297, 70, 1, 70, "Output"] }, Open ]], Cell[248982, 7301, 137, 3, 28, "SmallText"], Cell[249122, 7306, 515, 10, 110, "Input"], Cell[CellGroupData[{ Cell[249662, 7320, 58, 1, 30, "Input"], Cell[249723, 7323, 411, 12, 70, "Output"] }, Open ]], Cell[250149, 7338, 226, 5, 44, "SmallText"], Cell[250378, 7345, 144, 3, 50, "Input"], Cell[250525, 7350, 191, 4, 28, "SmallText"], Cell[250719, 7356, 191, 5, 70, "Input"], Cell[250913, 7363, 347, 6, 70, "Input"], Cell[251263, 7371, 219, 4, 50, "Input"], Cell[251485, 7377, 548, 10, 110, "Input"], Cell[252036, 7389, 197, 3, 50, "Input"], Cell[252236, 7394, 381, 7, 70, "Input"], Cell[252620, 7403, 281, 4, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[252938, 7412, 259, 9, 31, "Subsection"], Cell[253200, 7423, 122, 3, 28, "SmallText"], Cell[253325, 7428, 193, 4, 31, "Input"], Cell[253521, 7434, 193, 4, 31, "Input"], Cell[253717, 7440, 193, 4, 31, "Input"], Cell[CellGroupData[{ Cell[253935, 7448, 801, 15, 130, "Input"], Cell[254739, 7465, 46, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[254834, 7472, 275, 9, 31, "Subsection"], Cell[255112, 7483, 175, 4, 30, "Input"], Cell[255290, 7489, 175, 4, 30, "Input"], Cell[255468, 7495, 175, 4, 30, "Input"], Cell[255646, 7501, 89, 1, 30, "Input"], Cell[255738, 7504, 89, 1, 30, "Input"], Cell[255830, 7507, 89, 1, 30, "Input"], Cell[CellGroupData[{ Cell[255944, 7512, 759, 14, 130, "Input"], Cell[256706, 7528, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[256803, 7535, 260, 9, 31, "Subsection"], Cell[257066, 7546, 122, 3, 28, "SmallText"], Cell[257191, 7551, 214, 4, 31, "Input"], Cell[257408, 7557, 212, 4, 31, "Input"], Cell[CellGroupData[{ Cell[257645, 7565, 446, 7, 110, "Input"], Cell[258094, 7574, 48, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[258179, 7580, 450, 7, 110, "Input"], Cell[258632, 7589, 47, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[258728, 7596, 268, 9, 31, "Subsection"], Cell[258999, 7607, 122, 3, 28, "SmallText"], Cell[259124, 7612, 224, 4, 31, "Input"], Cell[259351, 7618, 229, 4, 31, "Input"], Cell[CellGroupData[{ Cell[259605, 7626, 449, 7, 110, "Input"], Cell[260057, 7635, 49, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[260143, 7641, 446, 7, 110, "Input"], Cell[260592, 7650, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[260689, 7657, 262, 9, 31, "Subsection"], Cell[260954, 7668, 203, 4, 30, "Input"], Cell[261160, 7674, 216, 4, 30, "Input"], Cell[261379, 7680, 230, 4, 30, "Input"], Cell[261612, 7686, 201, 4, 30, "Input"], Cell[261816, 7692, 214, 4, 30, "Input"], Cell[CellGroupData[{ Cell[262055, 7700, 469, 7, 110, "Input"], Cell[262527, 7709, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[262608, 7715, 465, 7, 90, "Input"], Cell[263076, 7724, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[263157, 7730, 471, 7, 110, "Input"], Cell[263631, 7739, 45, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[263725, 7746, 272, 9, 31, "Subsection"], Cell[264000, 7757, 203, 4, 30, "Input"], Cell[264206, 7763, 203, 4, 30, "Input"], Cell[264412, 7769, 203, 4, 30, "Input"], Cell[CellGroupData[{ Cell[264640, 7777, 751, 14, 130, "Input"], Cell[265394, 7793, 46, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[265489, 7800, 293, 9, 31, "Subsection"], Cell[265785, 7811, 108, 3, 28, "SmallText"], Cell[265896, 7816, 206, 3, 50, "Input"], Cell[266105, 7821, 194, 4, 30, "Input"], Cell[266302, 7827, 204, 4, 30, "Input"], Cell[266509, 7833, 92, 1, 30, "Input"], Cell[266604, 7836, 92, 1, 30, "Input"], Cell[266699, 7839, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[266833, 7845, 780, 14, 130, "Input"], Cell[267616, 7861, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[267713, 7868, 274, 9, 31, "Subsection"], Cell[267990, 7879, 102, 2, 28, "SmallText"], Cell[268095, 7883, 202, 3, 50, "Input"], Cell[268300, 7888, 190, 4, 30, "Input"], Cell[268493, 7894, 202, 4, 30, "Input"], Cell[268698, 7900, 92, 1, 30, "Input"], Cell[268793, 7903, 92, 1, 30, "Input"], Cell[268888, 7906, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[269022, 7912, 776, 14, 130, "Input"], Cell[269801, 7928, 47, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[269897, 7935, 266, 9, 31, "Subsection"], Cell[270166, 7946, 203, 4, 30, "Input"], Cell[270372, 7952, 203, 4, 30, "Input"], Cell[270578, 7958, 227, 4, 30, "Input"], Cell[270808, 7964, 92, 1, 30, "Input"], Cell[270903, 7967, 92, 1, 30, "Input"], Cell[270998, 7970, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[271132, 7976, 795, 15, 150, "Input"], Cell[271930, 7993, 45, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[272024, 8000, 280, 9, 31, "Subsection"], Cell[272307, 8011, 51, 1, 30, "Input"], Cell[272361, 8014, 275, 5, 91, "Input"], Cell[272639, 8021, 280, 5, 91, "Input"], Cell[272922, 8028, 207, 4, 90, "Input"], Cell[273132, 8034, 212, 4, 90, "Input"], Cell[273347, 8040, 91, 1, 30, "Input"], Cell[273441, 8043, 84, 1, 30, "Input"], Cell[273528, 8046, 1424, 28, 330, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[275001, 8080, 65, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[275091, 8085, 346, 8, 19, "Input", CellOpen->False], Cell[275440, 8095, 9474, 154, 70, "Output"] }, Open ]] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)