(************** 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[ 239398, 7642]*) (*NotebookOutlinePosition[ 240059, 7665]*) (* CellTagsIndexPosition[ 240015, 7661]*) (*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[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-06a\\outmath"\)], "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] = \(-\[Pi]\);\)\)], "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: .25 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 0.952381 0.196429 0.952381 [ [ 0 0 0 0 ] [ 1 .25 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .25 L 0 .25 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .97619 .19643 m .02381 .19643 L s .5 Mabswid .7381 .24405 m .7381 .14881 L s .5 .24405 m .5 .14881 L s .2619 .24405 m .2619 .14881 L s 0 0 0 r 2 Mabswid .5 .19643 m .30952 .19643 L s .37302 .16468 m .30952 .19643 L s .37302 .22817 m .30952 .19643 L s .5 .19643 m .5 .00595 L s .53175 .06944 m .5 .00595 L s .46825 .06944 m .5 .00595 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 72}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol008ioo`80091oo`00SWoo0`00Sgoo002>Ool3002?Ool008eoo`D008ioo`00SGoo 0`0000=oo`00Ool0SGoo002Ool2002@Ool0 08ioo`80091oo`00SWoo0P00T7oo002>Ool2002@Ool008ioo`80091oo`00SWoo0P00T7oo002>Ool2 002@Ool008ioo`80091oo`00SWoo0P00T7oo002>Ool2002@Ool008ioo`80091oo`00SWoo0P00T7oo 002>Ool2002@Ool008ioo`80091oo`00SWoo0P00T7oo002>Ool2002@Ool008ioo`80091oo`00SWoo 0P00T7oo002>Ool2002@Ool004]oo`03001oogoo041oo`8004=oo`03001oogoo04Yoo`00Bgoo00<0 07ooOol0@7oo0P00@goo00<007ooOol0BWoo001;Ool00`00Oomoo`10Ool20013Ool00`00Oomoo`1: Ool004]oo`03001oogoo01eoo`03001oogoo021oo`8004=oo`03001oogoo04Yoo`00Bgoo00<007oo Ool06goo10008Goo0P00@goo00<007ooOol0BWoo001;Ool00`00Oomoo`0IOol5000ROol20013Ool0 0`00Oomoo`1:Ool004]oo`03001oogoo01Moo`D002Aoo`8004=oo`03001oogoo04Yoo`00Bgoo00<0 07ooOol05Goo1@009Woo0P00@goo00<007ooOol0BWoo001;Ool00`00Oomoo`0COol5000XOol20013 Ool00`00Oomoo`1:Ool004]oo`03001oogoo015oo`D002Yoo`8004=oo`03001oogoo04Yoo`00Bgoo 00<007ooOol03goo1@00;7oo0P00@goo00<007ooOol0BWoo001;Ool00`00Oomoo`0=Ool5000^Ool2 0013Ool00`00Oomoo`1:Ool004]oo`03001oogoo00]oo`D0031oo`8004=oo`03001oogoo04Yoo`00 1gooo`004@002Goo0007Oooo000A0009Ool004]oo`03001oogoo00eoo`D002moo`03001oogoo045o o`03001oogoo04Yoo`00Bgoo00<007ooOol03goo1@00;Goo00<007ooOol0@Goo00<007ooOol0BWoo 001;Ool00`00Oomoo`0AOol5000[Ool00`00Oomoo`11Ool00`00Oomoo`1:Ool004]oo`03001oogoo 01=oo`D002Uoo`03001oogoo045oo`03001oogoo04Yoo`00Bgoo00<007ooOol05Goo1@009goo00<0 07ooOol0@Goo00<007ooOol0BWoo001;Ool00`00Oomoo`0GOol5000UOol00`00Oomoo`11Ool00`00 Oomoo`1:Ool004]oo`03001oogoo01Uoo`D002=oo`03001oogoo045oo`03001oogoo04Yoo`00Bgoo 00<007ooOol06goo10008Woo00<007ooOol0@Goo00<007ooOol0BWoo001;Ool00`00Oomoo`0MOol0 0`00Oomoo`0QOol00`00Oomoo`11Ool00`00Oomoo`1:Ool004]oo`03001oogoo045oo`03001oogoo 045oo`03001oogoo04Yoo`00Bgoo00<007ooOol0@Goo00<007ooOol0@Goo00<007ooOol0BWoo001; Ool00`00Oomoo`11Ool00`00Oomoo`11Ool00`00Oomoo`1:Ool004]oo`03001oogoo045oo`03001o ogoo045oo`03001oogoo04Yoo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {71, 0}} -> {-1.03055, -0.206252, 0.00369722, \ 0.00369722}}] }, Open ]] }, Closed]] }, 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]_] := \(-\[ScriptF]\) \((DiracDelta[\[Zeta] - L[1]\/2])\)\ 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]}, \[ScriptCapitalC][1]], sQ[1] \[Rule] Function[{\[Zeta]}, \(-\[ScriptF]\)\ \((\(-1\) + UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\) + \[ScriptCapitalC][2]], sM[1] \[Rule] Function[{\[Zeta]}, \[ScriptF]\ \[Zeta]\ \((\(-1\) + UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\) - 1\/2\ \[ScriptF]\ \[ScriptCapitalL]\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] - \[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], \[ScriptF] + \[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] \(-\[ScriptF]\) + sQo[1], \[ScriptCapitalC][3] \[Rule] sMo[1]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(bulksol = bulksolC /. fromCtoNQM\)], "Input"], Cell[BoxData[ \({sN[1] \[Rule] Function[{\[Zeta]}, sNo[1]], sQ[1] \[Rule] Function[{\[Zeta]}, \(-\[ScriptF]\)\ \((\(-1\) + UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\) + \((\(-\[ScriptF]\) + sQo[1])\)], sM[1] \[Rule] Function[{\[Zeta]}, \[ScriptF]\ \[Zeta]\ \((\(-1\) + UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\) - 1\/2\ \[ScriptF]\ \[ScriptCapitalL]\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] - \[Zeta]\ \((\(-\[ScriptF]\) + 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[{ SuperscriptBox[\(sN[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}], "==", "0"}]}, { RowBox[{ RowBox[{\(2\ \[ScriptF]\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]]\), "+", 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[ Derivative[ 1][ sN[ 1]][ \[Zeta]], 0], Equal[ Plus[ Times[ 2, \[ScriptF], DiracDelta[ Plus[ \[ScriptCapitalL], Times[ -2, \[Zeta]]]]], 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[{ {\(\(sN[1]\)[\[Zeta]] == \[ScriptCapitalC][1]\)}, {\(\[ScriptF]\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + \(sQ[ 1]\)[\[Zeta]] == \[ScriptF] + \[ScriptCapitalC][2]\)}, {\(\[Zeta]\ \((\[ScriptF] + \[ScriptCapitalC][2])\) + \(sM[ 1]\)[\[Zeta]] == \[ScriptF]\ \((\(-\(\[ScriptCapitalL]\/2\ \)\) + \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + \[ScriptCapitalC][3]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ sN[ 1][ \[Zeta]], \[ScriptCapitalC][ 1]], Equal[ Plus[ Times[ \[ScriptF], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], sQ[ 1][ \[Zeta]]], Plus[ \[ScriptF], \[ScriptCapitalC][ 2]]], Equal[ Plus[ Times[ \[Zeta], Plus[ \[ScriptF], \[ScriptCapitalC][ 2]]], sM[ 1][ \[Zeta]]], Plus[ Times[ \[ScriptF], Plus[ Times[ Rational[ -1, 2], \[ScriptCapitalL]], \[Zeta]], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], \[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[{ {\(\(sN[1]\)[\[Zeta]] == sNo[1]\)}, {\(\[ScriptF]\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + \(sQ[ 1]\)[\[Zeta]] == sQo[1]\)}, {\(\[Zeta]\ sQo[1] + \(sM[1]\)[\[Zeta]] == sMo[1] + \[ScriptF]\ \((\(-\(\[ScriptCapitalL]\/2\)\) + \ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ sN[ 1][ \[Zeta]], sNo[ 1]], Equal[ Plus[ Times[ \[ScriptF], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], sQ[ 1][ \[Zeta]]], sQo[ 1]], Equal[ Plus[ Times[ \[Zeta], sQo[ 1]], sM[ 1][ \[Zeta]]], Plus[ sMo[ 1], Times[ \[ScriptF], Plus[ Times[ Rational[ -1, 2], \[ScriptCapitalL]], \[Zeta]], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]]]]}], 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[""], "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 := {\(cerniera[1]\)[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[ \({\(ub\_d[1]\)["+"] == 0, \(ub\_n[1]\)["+"] == 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[ \({\(ub\_d[1]\)["+"] \[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[ \({\(cerniera[1]\)["+"], \(carrello[1]\)["-"]}\)], "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[ \({\(cerniera[1]\)["+"], \(carrello[1]\)["-"]}\)], "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: .27857 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 0.908163 0.816327 0.169898 0.816327 [ [ 0 0 0 0 ] [ 1 .27857 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .27857 L 0 .27857 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .90816 .1699 m .09184 .1699 L s 0 0 0 r .5 .1699 m .33673 .1699 L s .39116 .14269 m .33673 .1699 L s .39116 .19711 m .33673 .1699 L s .5 .1699 m .5 .00663 L s .52721 .06105 m .5 .00663 L s .47279 .06105 m .5 .00663 L s 0 g 1 Mabswid .02381 .1699 m .15986 .1699 L s .09184 .06786 m .09184 .27194 L s newpath .09184 .1699 .03265 0 365.73 arc s .84014 .1699 m .97619 .1699 L s .90816 .06786 m .90816 .27194 L s newpath .90816 .1699 .03265 0 365.73 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 80.1875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol008ioo`80091oo`00SWoo0`00Sgoo002>Ool3002?Ool008eoo`D008ioo`00SGoo 0`0000=oo`00Ool0SGoo002Eoo`03001oogoo01Yoo`006goo00<007ooOol0iGoo00<007ooOol0 6Woo000KOol00`00Oomoo`3UOol00`00Oomoo`0JOol001]oo`03001oogoo0>Eoo`03001oogoo01Yo o`006goo00<007ooOol0iGoo00<007ooOol06Woo000KOol00`00Oomoo`3UOol00`00Oomoo`0JOol0 01]oo`03001oogoo0>Eoo`03001oogoo01Yoo`006goo00<007ooOol0iGoo00<007ooOol06Woo000K Ool00`00Oomoo`3UOol00`00Oomoo`0JOol001]oo`03001oogoo0>Eoo`03001oogoo01Yoo`006goo 00<007ooOol0iGoo00<007ooOol06Woo000KOol00`00Oomoo`3UOol00`00Oomoo`0JOol001]oo`03 001oogoo0>Eoo`03001oogoo01Yoo`006goo00<007ooOol0iGoo00<007ooOol06Woo000KOol00`00 Oomoo`3UOol00`00Oomoo`0JOol001]oo`03001oogoo0>Eoo`03001oogoo01Yoo`006goo00<007oo Ool0iGoo00<007ooOol06Woo000KOol00`00Oomoo`3UOol00`00Oomoo`0JOol001]oo`03001oogoo 0>Eoo`03001oogoo01Yoo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {79.1875, 0}} -> {-1.1184, -0.208127, \ 0.00430941, 0.00430941}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[pltO, pltOa, pltOv, DisplayFunction \[Rule] $DisplayFunction, AspectRatio \[Rule] Automatic];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .2 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 0.896825 0.793651 0.163492 0.793651 [ [ 0 0 0 0 ] [ 1 .2 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .2 L 0 .2 L closepath clip newpath 0 g 2 Mabswid [ ] 0 setdash .89683 .16349 m .10317 .16349 L s 0 0 0 r .5 .16349 m .34127 .16349 L s .39418 .13704 m .34127 .16349 L s .39418 .18995 m .34127 .16349 L s .5 .16349 m .5 .00476 L s .52646 .05767 m .5 .00476 L s .47354 .05767 m .5 .00476 L s 0 g .10317 .16349 m .02381 .08413 L .18254 .08413 L .10317 .16349 L s 1 g .10317 .16349 m .10317 .16349 .03175 0 365.73 arc F 0 g newpath .10317 .16349 .03175 0 365.73 arc s .89683 .16349 m .81746 .08413 L .97619 .08413 L .89683 .16349 L s .81746 .06825 m .97619 .06825 L s 1 g .89683 .16349 m .89683 .16349 .03175 0 365.73 arc F 0 g newpath .89683 .16349 .03175 0 365.73 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 57.5625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgA000`40O003h00OSgoo00<007ooOol0 SWoo002>Ool2002@Ool008ioo`<008moo`00SWoo0`00Sgoo002=Ool5002>Ool008eoo`<00003Ool0 07oo08eoo`00S7oo100000=oo`000000SGoo002Ool2 002@Ool008ioo`8005Qoobl000Uoo`00SWoo0P00F7oo;`002Goo002>Ool2002@Ool008ioo`80091o o`00SWoo0P00T7oo0007Ool`001GOol2001HOol`0008Ool000Qoobh005Qoo`8005Uoobh000Uoo`00 2Goo0`009Woo0`00FGoo0P00FWoo0`009Woo0`002Woo000:Ool3000TOol3001JOol2001KOol3000T Ool3000;Ool000]oo`<0029oo`<005]oo`8005aoo`<0029oo`<000aoo`0037oo0`0087oo0`00G7oo 0P00GGoo0`0087oo0`003Goo000=Ool3000NOol3001MOol2001NOol3000NOol3000>Ool000ioo`<0 01aoo`<005ioo`8005moo`<001aoo`<000moo`003goo0`006Woo0`00Ggoo0P00H7oo0`006Woo0`00 47oo000@Ool3000HOol3001POol2001QOol3000HOol3000AOol0015oo`@001Eoo`<0065oo`80069o o`<001Eoo`@0019oo`004Woo10004goo0`00HWoo0P00Hgoo0`004goo10004goo000DOol3000AOol3 001SOol2001TOol3000AOol3000EOol001Eoo`<000Aoo`H000Eoo`<006Aoo`8006Eoo`<000Aoo`L0 00Aoo`<001Ioo`005Woo3`0000Aoo`00000004Qoo`03001oogoo01Yoo`8006Ioo`l00004Ool00000 000GOol001Moo`H000Aoo`L004Moo`@001]oo`8006Moo`H000Eoo`H001Qoo`0067oo0P002Woo0`00 AWoo1@0077oo0P00J7oo0P002Woo0`006Goo000GOol2000=Ool20013Ool5000NOol2001WOol2000= Ool2000HOol001Moo`03001oogoo00eoo`03001oogoo03ioo`H0021oo`8006Moo`03001oogoo00eo o`03001oogoo01Ioo`005Woo0P003Woo0P00?Woo1P008Woo0P00IWoo0P003goo0P005goo000FOol0 0`00Oomoo`0=Ool3000kOol5000UOol2001VOol2000@Ool00`00Oomoo`0EOol001Eoo`80011oo`80 03Uoo`D002Moo`8006Ioo`8000moo`8001Moo`005Goo0P0047ood00047oo0P005goo000EOol2000@ Ooo@000@Ool2000GOol001Eoo`80011oo`8003]oo`D008aoo`<000moo`8001Moo`005Woo00<007oo Ool03Woo0P00?Goo1000S7oo0P003goo0P005goo000FOol2000?Ool00`00Oomoo`0nOol4002;Ool2 000>Ool2000GOol001Moo`8000eoo`80045oo`D008Yoo`8000aoo`<001Moo`0067oo0P002goo0P00 A7oo1@00RGoo0P002Woo0`0067oo000HOol40007Ool30017Ool50027Ool40007Ool3000IOol001Uo o`D000Aoo`@004Uoo`@008Moo`@000Eoo`<001Yoo`006goo2@00CGoo00<007ooOol0R7oo2@006goo 000MOol6003JOol7000LOol00001\ \>"], ImageRangeCache->{{{0, 287}, {56.5625, 0}} -> {-1.13933, -0.206001, \ 0.00445529, 0.00445529}}] }, 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"}, {\(\(\[Theta]b[1]\)["+"]\)} }, RowSpacings->2, ColumnSpacings->1, RowAlignments->Baseline, ColumnAlignments->{Left}]} }, RowSpacings->4, ColumnSpacings->2, RowAlignments->Baseline, ColumnAlignments->{Left}], TableForm[ {{{ Subscript[ ub, d][ 1][ "-"], 0, \[Theta]b[ 1][ "-"]}, {0, 0, \[Theta]b[ 1][ "+"]}}}, TableSpacing -> {4, 2, 2}]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(vincoli // Simplify\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(ub\_d[1]\)["+"] == 0\)}, {\(\(ub\_n[1]\)["+"] == 0\)}, {\(\(ub\_n[1]\)["-"] == 0\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Equal[ Subscript[ ub, d][ 1][ "+"], 0], Equal[ Subscript[ ub, n][ 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]\)[ "+"] + \((\(-\(sN[1]\)[0]\) + \(sb\_d[1]\)["-"])\)\ \(wb\_d[1]\)[ "-"] + \((\(sN[1]\)[\[ScriptCapitalL]] + \(sb\_d[1]\)[ "+"])\)\ \(wb\_d[1]\)[ "+"] + \((\(-\(sQ[1]\)[0]\) + \(sb\_n[1]\)["-"])\)\ \(wb\_n[1]\)[ "-"] + \((\(sQ[1]\)[\[ScriptCapitalL]] + \(sb\_n[1]\)[ "+"])\)\ \(wb\_n[1]\)["+"]\)], "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[ \({\(ub\_d[1]\)["+"] == 0, \(ub\_n[1]\)["+"] == 0, \(ub\_n[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{ub = wb, \[Theta]b = \[Omega]b}, vincoli] // Simplify\)], "Input"], Cell[BoxData[ \({\(wb\_d[1]\)["+"] == 0, \(wb\_n[1]\)["+"] == 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[ \({\(wb\_d[1]\)["+"] \[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]\)["-"], \(\[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]\)[ "-"] + \((\(mb[1]\)[ "+"] - \(sM[1]\)[\[ScriptCapitalL]])\)\ \(\[Omega]b[1]\)[ "+"] + \((\(-\(sN[1]\)[0]\) + \(sb\_d[1]\)["-"])\)\ \(wb\_d[1]\)[ "-"]\)], "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, \(mb[1]\)["+"] - \(sM[1]\)[\[ScriptCapitalL]] == 0, \(-\(sN[1]\)[0]\) + \(sb\_d[1]\)["-"] == 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(eqbilbd /. bulksol // Simplify\)], "Input"], Cell[BoxData[ \({sMo[1] + \(mb[1]\)["-"] == 0, \[ScriptCapitalL]\ sQo[1] + \(mb[1]\)[ "+"] == \(\[ScriptF]\ \[ScriptCapitalL]\)\/2 + sMo[1], \(sb\_d[1]\)["-"] == sNo[1]}\)], "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}, {\(-1\), 0, \[ScriptCapitalL]}, {0, \(-1\), 0}}, {\(-\(mb[1]\)[ "-"]\), \(\[ScriptF]\ \[ScriptCapitalL]\)\/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"}, {\(-1\), "0", "\[ScriptCapitalL]"}, {"0", \(-1\), "0"} }], "\[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[{ {\(-\(mb[1]\)["-"]\)}, {\(\(\[ScriptF]\ \[ScriptCapitalL]\)\/2 - \(mb[1]\)["+"]\)}, {\(-\(sb\_d[1]\)["-"]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Times[ -1, mb[ 1][ "-"]], Plus[ Times[ Rational[ 1, 2], \[ScriptF], \[ScriptCapitalL]], 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[ \(3\)], "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[ \(3\)], "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[ \(3\)], "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] 3\n nf \[Rule] 3\n rango \ \[Rule] 3"\)], "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[ \("Vincoli giusti (le forze attive al bordo possono essere \ qualsiasi)"\)], "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]\)["-"] + \(mb[1]\)[ "+"]\ \(\[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[{ {\(\(mb[1]\)["-"]\)}, {\(\(mb[1]\)["+"]\)}, {\(\(sb\_d[1]\)["-"]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { mb[ 1][ "-"], 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[ \({\(mb[1]\)["-"], \(mb[1]\)["+"], \(sb\_d[1]\)["-"]}\)], "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, \(mb[1]\)["+"] \[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[ \({0, 0, 0}\)], "Output"] }, Open ]] }, Closed]], 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[ \({{0, 0, 0}}\)], "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, \[ScriptCapitalL]\ sQo[ 1] == \(\[ScriptF]\ \[ScriptCapitalL]\)\/2 + sMo[1], sNo[1] == 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[ \({sMo[1] \[Rule] 0, sNo[1] \[Rule] 0, sQo[1] \[Rule] \[ScriptF]\/2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[{\(sN[i]\)[\[Zeta]], \(sQ[i]\)[\[Zeta]], \(sM[i]\)[\[Zeta]]} /. bulksol, {i, 1, travi}] // Simplify\)], "Input"], Cell[BoxData[ \({{sNo[1], sQo[1] - \[ScriptF]\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]], sMo[1] - \[Zeta]\ sQo[ 1] + \[ScriptF]\ \((\(-\(\[ScriptCapitalL]\/2\)\) + \[Zeta])\)\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(cNQMval\)], "Input"], Cell[BoxData[ \({sMo[1] \[Rule] 0, sNo[1] \[Rule] 0, sQo[1] \[Rule] \[ScriptF]\/2}\)], "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] == \(\[ScriptCapitalY]\[ScriptCapitalJ]\ \(\[Epsilon][1]\)[\ \[Zeta]]\)\/\(\[ScriptCapitalL]\^2\ \[Kappa]\), sMo[1] + \[ScriptF]\ \((\(-\(\[ScriptCapitalL]\/2\)\) + \[Zeta])\)\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] == \[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[{\(sNo[1]\), "==", FractionBox[ RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_1[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], \(\[ScriptCapitalL]\^2\ \[Kappa]\)]}], ",", RowBox[{\(sMo[ 1] + \[ScriptF]\ \((\(-\(\[ScriptCapitalL]\/2\)\) + \[Zeta])\)\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\), "==", 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]}, \(\[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ sNo[1]\ \)\/\[ScriptCapitalY]\[ScriptCapitalJ] + \[ScriptCapitalD][1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(\[Zeta]\^2\ sMo[1]\)\/\(2\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) - \(\[Zeta]\^3\ sQo[1]\)\/\(6\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) + \(\[ScriptF]\ \[ScriptCapitalL]\^2\ \((\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \ \[Zeta]]\)\/\(16\ \[ScriptCapitalY]\[ScriptCapitalJ]\) - \(\[ScriptF]\ \ \[ScriptCapitalL]\ \((\(-\(\[ScriptCapitalL]\^2\/4\)\) + \[Zeta]\^2)\)\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\)\/\(4\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) + \(\[ScriptF]\ \((\(-\[ScriptCapitalL]\^3\) + 8\ \[Zeta]\ \^3)\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\)\/\(48\ \ \[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[{ FractionBox[ RowBox[{"\[ScriptCapitalY]\[ScriptCapitalJ]", " ", RowBox[{ SuperscriptBox[\(u\_1[1]\), "\[Prime]", MultilineFunction->None], "[", "\[Zeta]", "]"}]}], \(\[ScriptCapitalL]\^2\ \[Kappa]\)], "==", "0"}], ",", RowBox[{\(1\/2\ \[ScriptF]\ \((\(-\[Zeta]\) - \((\[ScriptCapitalL] - 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\), "==", 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]}, \[ScriptCapitalD][1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(1\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \)\)\((\(\[ScriptF]\ \[Zeta]\^3\)\/6 - 1\/8\ \[ScriptF]\ \[ScriptCapitalL]\^2\ \((\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + 1\/2\ \[ScriptF]\ \[ScriptCapitalL]\ \((\(-\(\ \[ScriptCapitalL]\^2\/4\)\) + \[Zeta]\^2)\)\ UnitStep[\(-\[ScriptCapitalL]\) \ + 2\ \[Zeta]] - 1\/24\ \[ScriptF]\ \((\(-\[ScriptCapitalL]\^3\) + 8\ \[Zeta]\^3)\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\) + \[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]\ sNo[1]\)\/\[ScriptCapitalY]\ \[ScriptCapitalJ] + \[ScriptCapitalD][ 1], \(\(1\/\(48\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\((\(-\ \[ScriptF]\)\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\^3\ UnitStep[\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta]] + 8\ \((3\ \[Zeta]\^2\ sMo[1] - \[Zeta]\^3\ sQo[1] + 6\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[ScriptCapitalD][2] + 6\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[Zeta]\ \ \[ScriptCapitalD][ 3])\))\)\), \(-\(\(\[ScriptF]\ \[ScriptCapitalL]\^2\ \((\ \[ScriptCapitalL] - 2\ \[Zeta])\)\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]]\)\/\(8\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\) + \(\[ScriptF]\ \[ScriptCapitalL]\ \ \((\[ScriptCapitalL]\^2 - 4\ \[Zeta]\^2)\)\ DiracDelta[\[ScriptCapitalL] - 2\ \ \[Zeta]]\)\/\(8\ \[ScriptCapitalY]\[ScriptCapitalJ]\) - \(\[ScriptF]\ \((\ \[ScriptCapitalL]\^3 - 8\ \[Zeta]\^3)\)\ DiracDelta[\[ScriptCapitalL] - 2\ \ \[Zeta]]\)\/\(24\ \[ScriptCapitalY]\[ScriptCapitalJ]\) + \(\(1\/\(8\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\((8\ \[Zeta]\ sMo[1] - 4\ \[Zeta]\^2\ sQo[ 1] + \[ScriptF]\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\^2\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + 8\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \[ScriptCapitalD][ 3])\)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(splist /. vinBer\) /. spsolD // Simplify\)], "Input"], Cell[BoxData[ \({\[ScriptCapitalD][ 1], \(-\(\(4\ \[ScriptF]\ \[Zeta]\^3 + \[ScriptF]\ \((\ \[ScriptCapitalL] - 2\ \[Zeta])\)\^3\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] - 48\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \((\[ScriptCapitalD][ 2] + \[Zeta]\ \[ScriptCapitalD][ 3])\)\)\/\(48\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\ \), \(\(1\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\)\)\((\(-\(1\/4\)\)\ \ \[ScriptF]\ \[ScriptCapitalL]\^2\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]] + 1\/4\ \[ScriptF]\ \[ScriptCapitalL]\ \((\[ScriptCapitalL]\^2 - 4\ \[Zeta]\^2)\)\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]] - 1\/12\ \[ScriptF]\ \((\[ScriptCapitalL]\^3 - 8\ \[Zeta]\^3)\)\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]] + 1\/4\ \[ScriptF]\ \((\(-2\)\ \[Zeta]\^2 + \((\[ScriptCapitalL] - \ 2\ \[Zeta])\)\^2\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\))\)\) + \[ScriptCapitalD][ 3]}\)], "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[ \({\[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[ \({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]}, \(\[ScriptCapitalL]\^2\ \[Zeta]\ \[Kappa]\ sNo[1]\ \)\/\[ScriptCapitalY]\[ScriptCapitalJ] + uo\_1[1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(\[Zeta]\^2\ sMo[1]\)\/\(2\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) - \(\[Zeta]\^3\ sQo[1]\)\/\(6\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) + \(\[ScriptF]\ \[ScriptCapitalL]\^2\ \((\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \ \[Zeta]]\)\/\(16\ \[ScriptCapitalY]\[ScriptCapitalJ]\) - \(\[ScriptF]\ \ \[ScriptCapitalL]\ \((\(-\(\[ScriptCapitalL]\^2\/4\)\) + \[Zeta]\^2)\)\ \ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\)\/\(4\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\) + \(\[ScriptF]\ \((\(-\[ScriptCapitalL]\^3\) + 8\ \[Zeta]\ \^3)\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]]\)\/\(48\ \ \[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]}, uo\_1[1]], u\_2[1] \[Rule] Function[{\[Zeta]}, \(-\(\(1\/\(2\ \[ScriptCapitalY]\[ScriptCapitalJ]\ \)\)\((\(\[ScriptF]\ \[Zeta]\^3\)\/6 - 1\/8\ \[ScriptF]\ \[ScriptCapitalL]\^2\ \((\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]] + 1\/2\ \[ScriptF]\ \[ScriptCapitalL]\ \((\(-\(\ \[ScriptCapitalL]\^2\/4\)\) + \[Zeta]\^2)\)\ UnitStep[\(-\[ScriptCapitalL]\) \ + 2\ \[Zeta]] - 1\/24\ \[ScriptF]\ \((\(-\[ScriptCapitalL]\^3\) + 8\ \[Zeta]\^3)\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\) + 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, \(u\_2[1]\)[0] == 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] == 0, \[ScriptCapitalL]\ \[Theta]o[1] + uo\_2[1] == \(\[ScriptF]\ \[ScriptCapitalL]\^3\)\/\(16\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\), uo\_2[1] == 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[{ {"1", "0", "0"}, {"0", "1", "\[ScriptCapitalL]"}, {"0", "1", "0"} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ColumnForm[matvin\[LeftDoubleBracket]2\[RightDoubleBracket]]\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {"0"}, {\(\(\[ScriptF]\ \[ScriptCapitalL]\^3\)\/\(16\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)}, {"0"} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {0, Times[ Rational[ 1, 16], \[ScriptF], 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[ \(3\)], "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[ \({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[ \({0, 0, \(\[ScriptF]\ \[ScriptCapitalL]\^2\)\/\(16\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)}\)], "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[ \({0, 0, \(\[ScriptF]\ \[ScriptCapitalL]\^2\)\/\(16\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)}\)], "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[ \({uo\_1[1] \[Rule] 0, uo\_2[1] \[Rule] 0, \[Theta]o[ 1] \[Rule] \(\[ScriptF]\ \[ScriptCapitalL]\^2\)\/\(16\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(\(splist /. vinBer\) /. spsol\) /. cRval // Simplify\) // Factor\) // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {"0"}, {\(-\(\(\[ScriptF]\ \((\(-3\)\ \[ScriptCapitalL]\^2\ \[Zeta] + 4\ \[Zeta]\^3 + \[ScriptCapitalL]\^3\ UnitStep[\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta]] - 6\ \[ScriptCapitalL]\^2\ \[Zeta]\ UnitStep[\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta]] + 12\ \[ScriptCapitalL]\ \[Zeta]\^2\ UnitStep[\(-\ \[ScriptCapitalL]\) + 2\ \[Zeta]] - 8\ \[Zeta]\^3\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\/\(48\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)\)}, {\(-\(\(\[ScriptF]\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\ \((\(-3\)\ \[ScriptCapitalL] - 6\ \[Zeta] + 2\ \[ScriptCapitalL]\^2\ DiracDelta[\[ScriptCapitalL] \ - 2\ \[Zeta]] - 8\ \[ScriptCapitalL]\ \[Zeta]\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]] + 8\ \[Zeta]\^2\ DiracDelta[\[ScriptCapitalL] - 2\ \[Zeta]] - 6\ \[ScriptCapitalL]\ UnitStep[\(-\[ScriptCapitalL]\) \ + 2\ \[Zeta]] + 12\ \[Zeta]\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\/\(48\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {0, Times[ Rational[ -1, 48], \[ScriptF], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], Plus[ Times[ -3, Power[ \[ScriptCapitalL], 2], \[Zeta]], Times[ 4, Power[ \[Zeta], 3]], Times[ Power[ \[ScriptCapitalL], 3], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], Times[ -6, Power[ \[ScriptCapitalL], 2], \[Zeta], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], Times[ 12, \[ScriptCapitalL], Power[ \[Zeta], 2], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], Times[ -8, Power[ \[Zeta], 3], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]]]], Times[ Rational[ -1, 48], \[ScriptF], Power[ \[ScriptCapitalY]\[ScriptCapitalJ], -1], Plus[ \[ScriptCapitalL], Times[ -2, \[Zeta]]], Plus[ Times[ -3, \[ScriptCapitalL]], Times[ -6, \[Zeta]], Times[ 2, Power[ \[ScriptCapitalL], 2], DiracDelta[ Plus[ \[ScriptCapitalL], Times[ -2, \[Zeta]]]]], Times[ -8, \[ScriptCapitalL], \[Zeta], DiracDelta[ Plus[ \[ScriptCapitalL], Times[ -2, \[Zeta]]]]], Times[ 8, Power[ \[Zeta], 2], DiracDelta[ Plus[ \[ScriptCapitalL], Times[ -2, \[Zeta]]]]], Times[ -6, \[ScriptCapitalL], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]], Times[ 12, \[Zeta], UnitStep[ Plus[ Times[ -1, \[ScriptCapitalL]], Times[ 2, \[Zeta]]]]]]]}], 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 = simplifyDirac[\[Zeta], 0, L[i]]]\)], "Input"], Cell[BoxData[ \(simplifyDirac[\[Zeta], 0, L[i]]\)], "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[ \({sMo[1] \[Rule] 0, sNo[1] \[Rule] 0, sQo[1] \[Rule] \[ScriptF]\/2}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Map[Factor, \(cRval // Simplify\) // extraSimplify, {2}]\)], "Input"], Cell[BoxData[ \({uo\_1[1] \[Rule] 0, uo\_2[1] \[Rule] 0, \[Theta]o[ 1] \[Rule] \(\[ScriptF]\ \[ScriptCapitalL]\^2\)\/\(16\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)}\)], "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\"\>", "0"} }, 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\"\>", \(1\/2\ \((\[ScriptF] - 2\ \[ScriptF]\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)} }, 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\"\>", \(1\/2\ \[ScriptF]\ \((\(-\[Zeta]\) - \((\ \[ScriptCapitalL] - 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$, TableDepth -> 2, TableAlignments -> Left]]]], "Output"] }, Open ]] }, Open ]] }, Open ]], 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\"\>", "0"} }, 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\"\>", \(-\(\(\[ScriptF]\ \((\(-3\)\ \[ScriptCapitalL]\ \^2\ \[Zeta] + 4\ \[Zeta]\^3 + \((\[ScriptCapitalL] - 2\ \ \[Zeta])\)\^3\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\/\(48\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)\)} }, 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\"\>", \(\(\[ScriptF]\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\ \((\[ScriptCapitalL] + 2\ \[Zeta] + 2\ \((\[ScriptCapitalL] - 2\ \[Zeta])\)\ UnitStep[\(-\[ScriptCapitalL]\) + 2\ \[Zeta]])\)\)\/\(16\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)\)} }, 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 = simplifyDirac[\[Zeta], 0, L[i]]\)} }, 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, \[ScriptF]\/2}\), \({0, \[ScriptF]\/2}\)} }, 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", "0"} }, 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 = {\[ScriptF] \[Rule] 50, \[ScriptCapitalY]\[ScriptCapitalJ] \[Rule] 10, \[Kappa] \[Rule] 0.01};\)\)], "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, \[ScriptF] \[Rule] 50, \[ScriptCapitalY]\[ScriptCapitalJ] \[Rule] 10, \[Kappa] \[Rule] 0.01`}\)], "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[ \({0, 0, \(\[ScriptF]\ \[ScriptCapitalL]\^2\)\/\(16\ \[ScriptCapitalY]\ \[ScriptCapitalJ]\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(spuv\[Theta][1]\)[L[1]] // Factor\)], "Input"], Cell[BoxData[ \({0, 0, \(\[ScriptF]\ \[ScriptCapitalL]\^2\ \((\(-3\) + 2\ \[ScriptCapitalL]\ \ DiracDelta[\[ScriptCapitalL]])\)\)\/\(48\ \ \[ScriptCapitalY]\[ScriptCapitalJ]\)}\)], "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[ \({0, \[ScriptF]\/2, 0}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(sNQM[1]\)[L[1]] // Simplify\) // Factor\)], "Input"], Cell[BoxData[ \({0, \(-\(\[ScriptF]\/2\)\), 0}\)], "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 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 1 .30902 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s 0 1 1 r .004 w .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 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 0.309017 0.0117721 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 1 .30902 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s 0 .4 1 r .004 w .02381 .60332 m .06244 .60332 L .10458 .60332 L .14415 .60332 L .18221 .60332 L .22272 .60332 L .26171 .60332 L .30316 .60332 L .34309 .60332 L .3815 .60332 L .42237 .60332 L .46172 .60332 L .48147 .60332 L .49012 .60332 L .49468 .60332 L .49719 .60332 L .49842 .60332 L .49955 .60332 L .50085 .01472 L .50154 .01472 L .50226 .01472 L .50471 .01472 L .5095 .01472 L .51896 .01472 L .53984 .01472 L .57781 .01472 L .61824 .01472 L .65714 .01472 L .6985 .01472 L .73835 .01472 L .77668 .01472 L .81746 .01472 L .85673 .01472 L .89448 .01472 L .93468 .01472 L .97337 .01472 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 0.603319 0.0471327 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .60332 m 1 .60332 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .60332 m .06244 .60332 L .10458 .60332 L .14415 .60332 L .18221 .60332 L .22272 .60332 L .26171 .60332 L .30316 .60332 L .34309 .60332 L .3815 .60332 L .42237 .60332 L .46172 .60332 L .49955 .60332 L .53984 .60332 L .57861 .60332 L .61984 .60332 L .65954 .60332 L .69774 .60332 L .73838 .60332 L .77751 .60332 L .81909 .60332 L .85916 .60332 L .89771 .60332 L .93871 .60332 L .97619 .60332 L s 1 0 .9 r .004 w .02381 .60332 m .06244 .55552 L .10458 .50339 L .14415 .45443 L .18221 .40734 L .22272 .35722 L .26171 .30898 L .30316 .2577 L .34309 .2083 L .3815 .16077 L .42237 .11021 L .46172 .06153 L .48147 .03708 L .49012 .02639 L .49468 .02074 L .49719 .01764 L .49842 .01612 L .49955 .01472 L .50085 .01521 L .50154 .01606 L .50226 .01695 L .50471 .01999 L .5095 .02592 L .51896 .03762 L .53984 .06345 L .57781 .11043 L .61824 .16044 L .65714 .20858 L .6985 .25976 L .73835 .30905 L .77668 .35648 L .81746 .40693 L .85673 .45552 L .89448 .50222 L .93468 .55196 L .97337 .59983 L .97619 .60332 L s 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]HGAYHf4PAg9QL6QYHgOol0 0`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0^Ool2O1a0Ool000moo`03001oogoo08ioo`03 001oogoo02ioo`030Imoogoo05eoo`03001oogoo02eoo`03O1aoog`L041oo`003goo00<007ooOol0 SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol0;7oo00El77ooOomoog`L03moo`003goo 00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol0:goo00=l77ooOol00goo 00=l77ooOol0?7oo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomo o`0ZOol00g`LOomoo`05Ool00g`LOomoo`0kOol000moo`03001oogoo08ioo`03001oogoo02ioo`03 0Imoogoo05eoo`03001oogoo02Uoo`03O1aoogoo00Moo`03O1aoogoo03Yoo`003goo00<007ooOol0 SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol0:7oo00=l77ooOol02Goo00=l77ooOol0 >Goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0XOol00g`L Oomoo`09Ool00g`LOomoo`0iOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eo o`03001oogoo02Moo`03O1aoogoo00]oo`03O1aoogoo03Qoo`003goo00<007ooOol0SWoo00<007oo Ool0;Woo00<1WgooOol0GGoo00<007ooOol09Woo00=l77ooOol03Goo00=l77ooOol0=goo000?Ool0 0`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0UOol00g`LOomoo`0?Ool0 0g`LOomoo`0fOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo 02Eoo`03O1aoogoo00moo`03O1aoogoo03Ioo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1 WgooOol0GGoo00<007ooOol097oo00=l77ooOol04Goo00=l77ooOol0=Goo000?Ool00`00Oomoo`2> Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0SOol00g`LOomoo`0COol00g`LOomoo`0d Ool000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo02=oo`03O1ao ogoo01=oo`03O1aoogoo03Aoo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo 00<007ooOol08Woo00=l77ooOol05Goo00=l77ooOol0Ool00`00Oomo o`0^Ool00`6OOomoo`1MOol00`00Oomoo`0QOol00g`LOomoo`0GOol00g`LOomoo`0bOol000moo`03 001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo021oo`03O1aoogoo01Uoo`03 O1aoogoo035oo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol0 7goo00=l77ooOol06goo00=l77ooOol0<7oo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6O Oomoo`1MOol00`00Oomoo`0NOol00g`LOomoo`0MOol00g`LOomoo`0_Ool000moo`03001oogoo08io o`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo01eoo`03O1aoogoo01moo`03O1aoogoo02io o`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol07Goo00=l77oo Ool087oo00=l77ooOol0;Goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol0 0`00Oomoo`0LOol00g`LOomoo`0QOol00g`LOomoo`0]Ool000moo`03001oogoo08ioo`03001oogoo 02ioo`030Imoogoo05eoo`03001oogoo01]oo`03O1aoogoo02=oo`03O1aoogoo02aoo`003goo00<0 07ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol06goo00=l77ooOol097oo00=l 77ooOol0:goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0J Ool00g`LOomoo`0VOol00g`LOomoo`0ZOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imo ogoo05eoo`03001oogoo01Uoo`03O1aoogoo02Qoo`03O1aoogoo02Uoo`003goo00<007ooOol0SWoo 00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol067oo00=l77ooOol0:Woo00=l77ooOol0:7oo 000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0GOol00g`LOomo o`0[Ool00g`LOomoo`0XOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03 001oogoo01Ioo`03O1aoogoo02eoo`03O1aoogoo02Moo`0037oo0`00H`?o0`00:7oo=00000<1W`00 0000 Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0DOol00g`LOomoo`0aOol00g`LOomoo`0U Ool000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo01=oo`03O1ao ogoo03=oo`03O1aoogoo02Aoo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo 00<007ooOol04goo00=l77ooOol0Ool00`00Oomo o`0^Ool00`6OOomoo`1MOol00`00Oomoo`0BOol00g`LOomoo`0eOol00g`LOomoo`0SOol000moo`03 001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo015oo`03O1aoogoo03Moo`03 O1aoogoo029oo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol0 47oo00=l77ooOol0>Goo00=l77ooOol08Goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6O Oomoo`1MOol00`00Oomoo`0?Ool00g`LOomoo`0kOol00g`LOomoo`0POol000moo`03001oogoo08io o`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo00moo`03O1aoogoo03]oo`03O1aoogoo021o o`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol03Woo00=l77oo Ool0?Goo00=l77ooOol07goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol0 0`00Oomoo`0=Ool00g`LOomoo`0oOol00g`LOomoo`0NOol000moo`03001oogoo08ioo`03001oogoo 02ioo`030Imoogoo05eoo`03001oogoo00aoo`03O1aoogoo045oo`03O1aoogoo01eoo`003goo00<0 07ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol02goo00=l77ooOol0@goo00=l 77ooOol077oo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`0; Ool00g`LOomoo`13Ool00g`LOomoo`0LOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imo ogoo05eoo`03001oogoo00Yoo`03O1aoogoo04Eoo`03O1aoogoo01]oo`003goo00<007ooOol0SWoo 00<007ooOol0;Woo00<1WgooOol0GGoo00<007ooOol02Goo00=l77ooOol0Agoo00=l77ooOol06Woo 000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`08Ool00g`LOomo o`19Ool00g`LOomoo`0IOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03 001oogoo00Moo`03O1aoogoo04]oo`03O1aoogoo01Qoo`003goo00<007ooOol0SWoo00<007ooOol0 ;Woo00<1WgooOol0GGoo00<007ooOol01goo00=l77ooOol0Bgoo00=l77ooOol067oo000?Ool00`00 Oomoo`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`06Ool00g`LOomoo`1=Ool00g`L Oomoo`0GOol000moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo00Eo o`03O1aoogoo04moo`03O1aoogoo01Ioo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1Wgoo Ool0GGoo00<007ooOol017oo00=l77ooOol0DGoo00=l77ooOol05Goo000?Ool00`00Oomoo`2>Ool0 0`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Oomoo`03Ool00g`LOomoo`1COol00g`LOomoo`0DOol0 00moo`03001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oogoo00=oo`03O1aoogoo 05=oo`03O1aoogoo01Aoo`003goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<0 07ooOol00Woo00=l77ooOol0EGoo00=l77ooOol04goo000?Ool00`00Oomoo`2>Ool00`00Oomoo`0^ Ool00`6OOomoo`1MOol01@00OomoogooO1`0FGoo00=l77ooOol04Woo000?Ool00`00Oomoo`2>Ool0 0`00Oomoo`0^Ool00`6OOomoo`1MOol01000Oomoog`LFgoo00=l77ooOol04Goo000?Ool00`00Oomo o`2>Ool00`00Oomoo`0^Ool00`6OOomoo`1MOol00`00Ooml701MOol00g`LOomoo`0@Ool000moo`03 001oogoo08ioo`03001oogoo02ioo`030Imoogoo05eoo`03001oog`L05eoo`03O1aoogoo011oo`00 3goo00<007ooOol0SWoo00<007ooOol0;Woo00<1WgooOol0GGoo00<007`LOol0GWoo00=l77ooOol0 3goo000?Ool00`00Oomoo`2>Oolb0ImLOol300000g`L0000001O000017`L000000003Goo000?Ool0 0`00Oomoo`2>Ool00`00Oomoo`2>Ool00`00Oomoo`1`Ool000moo`03001oogoo08ioo`03001oogoo 08ioo`03001oogoo071oo`00ogooYGoo0000\ \>"], ImageRangeCache->{{{0, 419}, {67.25, 0}} -> {-0.0960041, -0.0122006, \ 0.00761817, 0.00761817}, {{12.5625, 116.188}, {65.625, 1.5625}} -> \ {-0.152298, -1.10361, 0.0101328, 0.0327904}, {{157.625, 261.313}, {65.625, \ 1.5625}} -> {-1.62187, -27.5819, 0.0101298, 0.819513}, {{302.75, 406.375}, \ {65.625, 1.5625}} -> {-3.09271, -13.1352, 0.0101328, 0.204747}}] }, 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 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 1 .30902 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s 1 .9 0 r .004 w .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 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 0.367725 0.00408753 0.632275 0.167589 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0147151 5.65061 [ [ 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 .6 0 r .004 w .02381 .01472 m .06244 .08619 L .10458 .16304 L .14415 .23309 L .18221 .29757 L .22272 .36206 L .26171 .41911 L .30316 .47324 L .34309 .51798 L .3815 .55318 L .40095 .56777 L .42237 .58113 L .44268 .59104 L .46172 .59777 L .46668 .5991 L .4721 .60035 L .47687 .60127 L .48196 .60207 L .48456 .6024 L .487 .60267 L .48938 .60288 L .49157 .60304 L .49365 .60316 L .49472 .60321 L .49585 .60325 L .497 .60328 L .49806 .60331 L .49933 .60332 L .50049 .60332 L .50167 .60331 L .50277 .60329 L .50399 .60326 L .5053 .60321 L .50659 .60315 L .50796 .60307 L .5104 .6029 L .51478 .60248 L .51957 .60185 L .52477 .60097 L .53033 .59981 L .54033 .59716 L .56168 .58915 L .58183 .57874 L .6203 .55172 L .66122 .51354 L .70062 .46862 L .73851 .41881 L .77885 .35966 L .81767 .29777 L .85895 .2277 L Mistroke .89871 .15711 L .93695 .0873 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 0.71164 0.00408753 0.97619 0.167589 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.941766 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 1 .30902 L s .02381 0 m .02381 .61803 L s 0 0 0 r .5 Mabswid .02381 .30902 m .06244 .30902 L .10458 .30902 L .14415 .30902 L .18221 .30902 L .22272 .30902 L .26171 .30902 L .30316 .30902 L .34309 .30902 L .3815 .30902 L .42237 .30902 L .46172 .30902 L .49955 .30902 L .53984 .30902 L .57861 .30902 L .61984 .30902 L .65954 .30902 L .69774 .30902 L .73838 .30902 L .77751 .30902 L .81909 .30902 L .85916 .30902 L .89771 .30902 L .93871 .30902 L .97619 .30902 L s .68 1 0 r .004 w .02381 .60332 m .02499 .60332 L .02605 .60331 L .02729 .6033 L .02846 .60329 L .03053 .60326 L .03279 .60321 L .03527 .60315 L .0379 .60306 L .04262 .60286 L .04749 .60259 L .05205 .60228 L .06244 .60138 L .07305 .60017 L .08274 .59881 L .10458 .59485 L .12357 .5904 L .14429 .58448 L .18493 .56962 L .22406 .55127 L .26565 .52741 L .30571 .50018 L .34426 .47004 L .38527 .43375 L .42475 .39468 L .46273 .35329 L .50315 .30514 L .54206 .25933 L .58342 .21494 L .62326 .17637 L .66159 .14317 L .70238 .11202 L .74164 .08611 L .77939 .06498 L .8196 .04654 L .85828 .03276 L .87793 .02725 L .89942 .02236 L .90935 .02051 L .91995 .01882 L .92989 .0175 L .93905 .01651 L .94822 .01573 L .95295 .01542 L .95815 .01514 L .96268 .01495 L .96691 .01483 L .96925 .01478 L .97139 .01475 L .97257 .01473 L Mistroke .97385 .01472 L .97506 .01472 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 % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{420, 72.0625}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00=Gh7ooOol0>7oo000?Ool0 0`00Oomoo`2;Ool00`00Oomoo`09Ool00giPOomoo`1=Ool00giPOomoo`0_Ool00`00Oomoo`0jOol0 0eOPOomoo`0iOol000moo`03001oogoo08]oo`03001oogoo00Uoo`03OV1oogoo04aoo`03OV1oogoo 031oo`03001oogoo03Uoo`03En1oogoo03Yoo`003goo00<007ooOol0Rgoo00<007ooOol02Woo00=n H7ooOol0BWoo00=nH7ooOol07oo00=Gh7ooOol0>goo000?Ool00`00Oomoo`2; Ool00`00Oomoo`0;Ool00giPOomoo`19Ool00giPOomoo`0aOol00`00Oomoo`0hOol00eOPOomoo`0k Ool000moo`03001oogoo08]oo`03001oogoo00]oo`03OV1oogoo04Qoo`03OV1oogoo039oo`03001o ogoo03Moo`03En1oogoo03aoo`003goo00<007ooOol0Rgoo00<007ooOol037oo00=nH7ooOol0Agoo 00=nH7ooOol0Ool00giP Oomoo`13Ool00giPOomoo`0dOol00`00Oomoo`0cOol00eOPOomoo`10Ool000aoo`<006UoP08002=o o`03001oogoo00moo`03OV1oogoo045oo`03OV1oogoo03=oocL00003En00000003@000eoo`003goo 00<007ooOol0Rgoo00<007ooOol03goo00=nH7ooOol0@Goo00=nH7ooOol0=Goo00<007ooOol07oo00=nH7ooOol0>Goo00<007ooOol0:goo00=Gh7ooOol0B7oo000?Ool0 0`00Oomoo`2;Ool00`00Oomoo`0DOol00giPOomoo`0gOol00giPOomoo`0jOol00`00Oomoo`0ZOol0 0eOPOomoo`19Ool000moo`03001oogoo08]oo`03001oogoo01Eoo`03OV1oogoo03Eoo`03OV1oogoo 03]oo`03001oogoo02Uoo`03En1oogoo04Yoo`003goo00<007ooOol0Rgoo00<007ooOol05Woo00=n H7ooOol0=7oo00=nH7ooOol0>goo00<007ooOol0:7oo00=Gh7ooOol0Bgoo000?Ool00`00Oomoo`2; Ool00`00Oomoo`0FOol00giPOomoo`0cOol00giPOomoo`0lOol00`00Oomoo`0WOol00eOPOomoo`1< Ool000moo`03001oogoo08]oo`03001oogoo01Moo`03OV1oogoo035oo`03OV1oogoo03eoo`03001o ogoo02Moo`03En1oogoo04aoo`003goo00<007ooOol0Rgoo00<007ooOol067oo00=nH7ooOol0;goo 00=nH7ooOol0?Woo00<007ooOol09Woo00=Gh7ooOol0CGoo000?Ool00`00Oomoo`2;Ool00`00Oomo o`0HOol00giPOomoo`0^Ool00giPOomoo`0oOol00`00Oomoo`0UOol00eOPOomoo`1>Ool000moo`03 001oogoo08]oo`03001oogoo01Uoo`03OV1oogoo02eoo`03OV1oogoo03moo`03001oogoo02Aoo`03 En1oogoo04moo`003goo00<007ooOol0Rgoo00<007ooOol06Woo00=nH7ooOol0:goo00=nH7ooOol0 @7oo00<007ooOol08Woo0UOPDWoo000?Ool00`00Oomoo`2;Ool00`00Oomoo`0JOol00giPOomoo`0Z Ool00giPOomoo`11Ool00`00Oomoo`0QOol00eOPOomoo`1BOol000moo`03001oogoo08]oo`03001o ogoo01]oo`03OV1oogoo02Qoo`03OV1oogoo049oo`03001oogoo021oo`03En1oogoo05=oo`003goo 00<007ooOol0Rgoo00<007ooOol077oo00=nH7ooOol09Woo00=nH7ooOol0@goo00<007ooOol07goo 00=Gh7ooOol0E7oo000?Ool00`00Oomoo`2;Ool00`00Oomoo`0MOol00giPOomoo`0UOol00giPOomo o`13Ool00`00Oomoo`0MOol2En1GOol000moo`03001oogoo08]oo`03001oogoo01ioo`03OV1oogoo 02=oo`03OV1oogoo04Aoo`03001oogoo01aoo`03En1oogoo05Moo`003goo00<007ooOol0Rgoo00<0 07ooOol07goo00=nH7ooOol08Goo00=nH7ooOol0AGoo00<007ooOol06goo00=Gh7ooOol0F7oo000? Ool00`00Oomoo`2;Ool00`00Oomoo`0POol00giPOomoo`0OOol00giPOomoo`16Ool00`00Oomoo`0I Ool2En1KOol000moo`03001oogoo08]oo`03001oogoo025oo`03OV1oogoo01eoo`03OV1oogoo04Mo o`03001oogoo01Qoo`03En1oogoo05]oo`003goo00<007ooOol0Rgoo00<007ooOol08Woo00=nH7oo Ool06goo00=nH7ooOol0B7oo00<007ooOol05Woo0UOPGWoo000?Ool00`00Oomoo`2;Ool00`00Oomo o`0SOol00giPOomoo`0IOol00giPOomoo`19Ool00`00Oomoo`0DOol2En1POol000moo`03001oogoo 08]oo`03001oogoo02Aoo`03OV1oogoo01Moo`03OV1oogoo04Yoo`03001oogoo01=oo`03En1oogoo 061oo`003goo00<007ooOol0Rgoo00<007ooOol09Goo0WiP5Woo00=nH7ooOol0Bgoo00<007ooOol0 4Goo0UOPHgoo000?Ool00`00Oomoo`2;Ool00`00Oomoo`0WOol2OV0BOol2OV1>Ool00`00Oomoo`0= Ool4En1UOol000moo`03001oogoo08]oo`03001oogoo02Uoo`03OV1oogoo00ioo`03OV1oogoo04io o`03001oogoo00Yoo`=Gh6Uoo`003goo00<007ooOol0Rgoo00<007ooOol0:Woo0WiP2goo0giPDGoo 00<007ooOol01Woo15OPK7oo000?Ool00`00Oomoo`2;Ool00`00Oomoo`0/Ool;OV1DOol9En1`Ool0 00moo`03001oogoo08]oo`03001oogoo08]oo`03001oogoo07Ioo`003goo00<007ooOol0Rgoo00<0 07ooOol0Rgoo00<007ooOol0MWoo003oOonUOol00001\ \>"], ImageRangeCache->{{{0, 419}, {71.0625, 0}} -> {-0.0943298, -0.0128784, \ 0.00761017, 0.00761017}, {{12.375, 121.875}, {69.3125, 1.6875}} -> {-0.14414, \ -1.10435, 0.00959613, 0.0310537}, {{154.75, 264.25}, {69.3125, 1.6875}} -> \ {-1.51039, -0.00543512, 0.00959613, 0.00161738}, {{297.063, 406.563}, \ {69.3125, 1.6875}} -> {-2.87604, -0.345111, 0.00959613, 0.00970429}}] }, 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[ \({\(-1.`\), 0.`}\)], "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 \(\@\( xDiag . xDiag\)\) \((e\_2)\)\)], "Input"], Cell[BoxData[ \({0, 0}\)], "Output"] }, Open ]], Cell[BoxData[ RowBox[{ RowBox[{"mU", "=", RowBox[{"(", GridBox[{ {"1.2", "0"}, {"0", "512"} }], ")"}]}], ";"}]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \({\((xUpperR - xLowerL)\), xC}\)], "Input"], Cell[BoxData[ \({{1.2012`, 0.512`}, {\(-0.5`\), 0.`}}\)], "Output"] }, Open ]] }, Closed]], 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: .42624 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 0.896429 0.792858 0.21312 0.792858 [ [ 0 0 0 0 ] [ 1 .42624 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .01015 m .02381 .41609 L .97619 .41609 L .97619 .01015 L F 0 g .008 w .02381 .01015 Mdot .97619 .41609 Mdot 2 Mabswid [ ] 0 setdash .89643 .21312 m .10357 .21312 L s .5 Mabswid .69821 .25276 m .69821 .17348 L s .5 .25276 m .5 .17348 L s .30179 .25276 m .30179 .17348 L s 0 0 0 r .5 .21312 m .34143 .21312 L s .39429 .18669 m .34143 .21312 L s .39429 .23955 m .34143 .21312 L s .5 .21312 m .5 .05455 L s .52643 .10741 m .5 .05455 L s .47357 .10741 m .5 .05455 L s 0 g 1 Mabswid .0375 .21312 m .16964 .21312 L s .10357 .11401 m .10357 .31223 L s newpath .10357 .21312 .03171 0 365.73 arc s .83036 .21312 m .9625 .21312 L s .89643 .11401 m .89643 .31223 L s newpath .89643 .21312 .03171 0 365.73 arc s 1 0 0 r .5 Mabswid .89643 .21312 m .86427 .20309 L .82919 .19231 L .79624 .18248 L .76456 .17343 L .73084 .16438 L .69838 .15638 L .66387 .14878 L .63063 .14251 L .59865 .13757 L .58246 .13552 L .56463 .13364 L .54772 .13225 L .53187 .13131 L .52774 .13112 L .52323 .13095 L .51925 .13082 L .51502 .13071 L .51286 .13066 L .51082 .13062 L .50884 .13059 L .50702 .13057 L .50528 .13055 L .5044 .13055 L .50345 .13054 L .5025 .13054 L .50161 .13053 L .50056 .13053 L .49959 .13053 L .49861 .13053 L .49769 .13054 L .49668 .13054 L .49559 .13055 L .49451 .13055 L .49337 .13057 L .49134 .13059 L .48769 .13065 L .48371 .13074 L .47938 .13086 L .47475 .13102 L .46642 .13139 L .44865 .13252 L .43188 .13398 L .39985 .13777 L .36579 .14313 L .33298 .14943 L .30144 .15642 L .26786 .16472 L .23554 .1734 L .20118 .18323 L Mistroke .16808 .19314 L .13624 .20294 L .10357 .21312 L Mfstroke .68892 .19598 m .70751 .1167 L s .5 .17017 m .5 .09089 L s .31108 .19598 m .29249 .1167 L s 0 g 1 Mabswid .0375 .21312 m .16964 .21312 L s .10357 .11401 m .10357 .31223 L s newpath .10357 .21312 .03171 0 365.73 arc s .83036 .21312 m .9625 .21312 L s .89643 .11401 m .89643 .31223 L s newpath .89643 .21312 .03171 0 365.73 arc s 0 0 m 1 0 L 1 .42624 L 0 .42624 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 122.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooR7>L00<007>LLi`0QG>L2Goo0007Oon7Li`30026Li`9Ool000Mo ohMcW0<008IcW0Uoo`001gooQW>L00D007>L001cW00008EcW0Uoo`001gooQW>L00D007>L001cW000 08EcW0Uoo`001gooQG>L00@007>LLi`0009cW003001cW7>L089cW0Uoo`001gooQG>L00@007>LLi`0 009cW003001cW7>L089cW0Uoo`001gooQ7>L00D007>LLiacW00000=cW003001cW7>L085cW0Uoo`00 1gooQ7>L00D007>LLiacW00000=cW003001cW7>L085cW0Uoo`001gooPg>L00<007>LLi`00W>L00<0 07>LLi`00W>L00<007>LLi`0P7>L2Goo0007Oon3Li`00`00LiacW002Li`00`00LiacW002Li`00`00 LiacW020Li`9Ool000Mooh9cW003001cW7>L00=cW003O01cW7>L00=cW003001cW7>L07mcW0Uoo`00 1gooPW>L00<007>LLi`00g>L00=l07>LLi`00g>L00<007>LLi`0Og>L2Goo0007Oon1Li`00`00Liac W004Li`00g`0LiacW004Li`00`00LiacW01nLi`9Ool000Mooh5cW003001cW7>L00AcW003O01cW7>L 00AcW003001cW7>L07icW0Uoo`001gooP7>L00<007>LLi`01G>L00=l07>LLi`01G>L00<007>LLi`0 OG>L2Goo0007Oon8Li`00g`0LiacW025Li`9Ool000MooaMcW003001cW7>L06icW003O01cW7>L06ic W003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0L00=l07>LLi`0>7>L00=l07>LLi`0>7>L 00=l07>LLi`0L00<007>LLi`057>L2Goo0007OolGLi`00`00LiacW00cLi`00g`0LiacW00hLi`0 0g`0LiacW00hLi`00g`0LiacW00cLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L03=cW003 O01cW7>L03QcW003O01cW7>L03QcW003O01cW7>L03=cW003001cW7>L01AcW0Uoo`001goo5g>L00<0 07>LLi`0=7>L00=l07>LLi`0=g>L00=l07>LLi`0=g>L00=l07>LLi`0=7>L00<007>LLi`057>L2Goo 0007OolGLi`00`00LiacW00dLi`00g`0LiacW00[Li`HO00^Li`00g`0LiacW00dLi`00`00LiacW00D Li`9Ool000MooaMcW003001cW7>L03AcW003O01cW7>L021cW0]l00acW003O01cW7>L00UcW0il021c W003O01cW7>L03AcW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0=7>L00=l07>LLi`067>L 27`05g>L00=l07>LLi`05g>L1g`06G>L00=l07>LLi`0=7>L00<007>LLi`057>L2Goo0007OolGLi`0 0`00LiacW00eLi`00g`0LiacW00CLi`4O00OLi`00g`0LiacW00NLi`7O00ALi`00g`0LiacW00eLi`0 0`00LiacW00DLi`9Ool000MooaMcW003001cW7>L03EcW003O01cW7>L00acW0Ml02=cW003O01cW7>L 02EcW0El00acW003O01cW7>L03EcW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0=G>L00=l 07>LLi`017>L27`0:W>L00=l07>LLi`0:W>L1G`01g>L00=l07>LLi`0=G>L00<007>LLi`057>L2Goo 0007OolGLi`00`00LiacW00eLi`00g`0LiacW004O00bLi`00g`0LiacW00_Li`5O002Li`00g`0Liac W00eLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L03AcW0Al03IcW003O01cW7>L03AcW0Al 03IcW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0L0g`00W>L00=l07>LLi`0=G>L00=l 07>LLi`0=G>L00=l07>LLi`00g`0L00<007>LLi`057>L2Goo0007OolGLi`00`00LiacW00^Li`3 O005Li`00g`0LiacW00eLi`00g`0LiacW00eLi`00g`0LiacW003Li`3O00`Li`00`00LiacW00DLi`9 Ool000MooaMcW003001cW7>L02YcW0Al00QcW003O01cW7>L03EcW003O01cW7>L03EcW003O01cW7>L 00IcW0Al02acW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`09G>L1G`037>L00=l07>LLi`0 =G>L00=l07>LLi`0=G>L00=l07>LLi`02W>L1G`09g>L00<007>LLi`057>L2Goo0007OolGLi`00`00 LiacW00QLi`4O00@Li`00`00O01cW00fLi`00`00LiacW00eLi`00g`0001cW00?Li`4O00SLi`00`00 LiacW00DLi`9Ool000MooaMcW003001cW7>L01icW0=l01AcW003001cW7`003IcW003001cW7>L03Ac W003O01cW00001AcW0=l021cW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`06g>L0g`05g>L 00<007>LO000=W>L00<007>LLi`0=7>L00=l07>L00005g>L0g`07G>L00<007>LLi`057>L2Goo0007 OolDLi`6000HLi`3O00JLi`00`00Lial000fLi`00`00LiacW00dLi`00g`0Li`0000JLi`3O00GLi`7 000CLi`9Ool000Mooa9cW08000=cW003001cW7>L008001=cW0=l01ecW003001cW7`001QcW003001c W7>L01]cW003001cW7>L03AcW003O01cW00001ecW0=l01=cW005001cW7>LLi`00003Li`00`00Liac W00@Li`9Ool000Mooa5cW003001cW7>L00=cW003001cW7>L009cW08000ecW0Al021cW004001cW7>L O00ELi`2000NLi`00`00LiacW00cLi`017`0LiacW00087>L0g`03W>L0P0017>L00<007>LLi`00W>L 0P0047>L2Goo0007Ool@Li`00`00LiacW004Li`00`00LiacW004Li`00`00LiacW007Li`3O00TLi`0 1000LiacW7`04g>L0P0087>L00<007>LLi`0L00Al07>LLi`002=cW0=l00YcW003001cW7>L00Ac W003001cW7>L00AcW003001cW7>L00ecW0Uoo`001goo47>L00<007>LLi`017>L00<007>LLi`01G>L 00<007>LLi`00g>L0g`09g>L00@007>LLial015cW080029cW003001cW7>L03=cW004O01cW7>L000V Li`3O007Li`00`00LiacW004Li`00`00LiacW005Li`00`00LiacW00L00EcW003001cW7>L00EcW003001cW7>L00=l02YcW003001cW7>L011cW08002AcW003001cW7>L 03IcW003001cW7>L02McW0Al009cW003001cW7>L00EcW003001cW7>L00EcW003001cW7>L00acW0Uo o`001goo3W>L00<007>LLi`01W>L00<007>LLi`01G>L00<007`0O000;G>L00<007>LLi`03W>L0P00 9W>L00<007>LLi`0=W>L00<007>LLi`0:g>L00=l0000O0001g>L00<007>LLi`01W>L00<007>LLi`0 2g>L2Goo0007Ool>Li`00`00LiacW006Li`00`00LiacW002Li`3O0000`00LiacW00]Li`00`00Liac W00L00IcW003001cW7`0009l00AcW003001cW7>L 02acW003001cW7>L00YcW08002YcW003001cW7>L03IcW003001cW7>L02acW003001cW7>L009cW0=l 0003Li`007>L00McW003001cW7>L00]cW0Uoo`001goo17>Lo`002P000g>L2Goo0007Ool>Li`00`00 LiacW005LicT0008Li`00`00LiacW00;Li`9Ool000Moo`icW003001cW7>L00IcW003001cW7>L00Ec W003001cW7>L02ecW003001cW7>L00ecW08002McW003001cW7>L03IcW003001cW7>L02acW003001c W7>L00IcW003001cW7>L00IcW003001cW7>L00]cW0Uoo`001goo3W>L00<007>LLi`01W>L00<007>L Li`01G>L00<007>LLi`0;G>L00<007>LLi`03g>L0P009G>L00<007>LLi`0=W>L00<007>LLi`0;G>L 00<007>LLi`01G>L00<007>LLi`01W>L00<007>LLi`02g>L2Goo0007Ool?Li`00`00LiacW005Li`0 0`00LiacW004Li`00`00LiacW00^Li`00`00LiacW00ALi`2000SLi`00`00LiacW00fLi`00`00Liac W00^Li`00`00LiacW004Li`00`00LiacW005Li`00`00LiacW00L 00EcW003001cW7>L00AcW003001cW7>L02icW003001cW7>L01=cW080025cW003001cW7>L03IcW003 001cW7>L02icW003001cW7>L00AcW003001cW7>L00EcW003001cW7>L00acW0Uoo`001goo47>L00<0 07>LLi`017>L00<007>LLi`00g>L00<007>LLi`0;g>L00<007>LLi`05G>L0P007g>L00<007>LLi`0 =W>L00<007>LLi`0;g>L00<007>LLi`00g>L00<007>LLi`017>L00<007>LLi`03G>L2Goo0007OolA Li`20004Li`00`00LiacW002Li`00`00LiacW00`Li`00`00LiacW00GLi`2000MLi`00`00LiacW00f Li`00`00LiacW00`Li`20003Li`00`00LiacW002Li`2000@Li`9Ool000Mooa=cW0<00004Li`007>L Li`2000cLi`00`00LiacW00fLi`00`00LiacW00fLi`00`00LiacW00bLi`200000g>L001cW002Li`0 0`00LiacW00@Li`9Ool000MooaIcW0@003EcW003001cW7>L03IcW003001cW7>L03IcW003001cW7>L 03AcW0D001=cW0Uoo`001goo5g>L00<007>LLi`0=G>L00<007>LLi`0=W>L00<007>LLi`0=W>L00<0 07>LLi`0=G>L00<007>LLi`057>L2Goo0007OolGLi`00`00LiacW00eLi`00`00LiacW00fLi`00`00 LiacW00fLi`00`00LiacW00eLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L0=mcW003001c W7>L01AcW0Uoo`001goo5g>L00<007>LLi`0gg>L00<007>LLi`057>L2Goo0007OolGLi`00`00Liac W03OLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L0=mcW003001cW7>L01AcW0Uoo`001goo 5g>L00<007>LLi`0gg>L00<007>LLi`057>L2Goo0007OolGLi`00`00LiacW03OLi`00`00LiacW00D Li`9Ool000MooaMcW003001cW7>L0=mcW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0gg>L 00<007>LLi`057>L2Goo0007OolGLi`00`00LiacW03OLi`00`00LiacW00DLi`9Ool000MooaMcW003 001cW7>L0=mcW003001cW7>L01AcW0Uoo`001goo5g>L00<007>LLi`0gg>L00<007>LLi`057>L2Goo 0007OolGLi`00`00LiacW03OLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L0=mcW003001c W7>L01AcW0Uoo`001goo5g>L00<007>LLi`0gg>L00<007>LLi`057>L2Goo0007OolGLi`00`00Liac W03OLi`00`00LiacW00DLi`9Ool000MooaMcW003001cW7>L0=mcW003001cW7>L01AcW0Uoo`001goo 5g>L00<007>LLi`0gg>L00<007>LLi`057>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW11cW003001oogoo00Moo`001gooog>L47>L00<007ooOol01goo003oOolQOol00?mo ob5oo`00\ \>"], ImageRangeCache->{{{0, 287}, {121.75, 0}} -> {-1.13365, -0.268802, \ 0.00441565, 0.00441565}}] }, 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: .42624 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 0.896429 0.792858 0.21312 0.792858 [ [ 0 0 0 0 ] [ 1 .42624 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .01015 m .02381 .41609 L .97619 .41609 L .97619 .01015 L F 0 g .008 w .02381 .01015 Mdot .97619 .41609 Mdot 2 Mabswid [ ] 0 setdash .89643 .21312 m .10357 .21312 L s .5 Mabswid .69821 .25276 m .69821 .17348 L s .5 .25276 m .5 .17348 L s .30179 .25276 m .30179 .17348 L s 0 0 0 r .5 .21312 m .34143 .21312 L s .39429 .18669 m .34143 .21312 L s .39429 .23955 m .34143 .21312 L s .5 .21312 m .5 .05455 L s .52643 .10741 m .5 .05455 L s .47357 .10741 m .5 .05455 L s 0 g 2 Mabswid .10357 .21312 m .02429 .13383 L .18286 .13383 L .10357 .21312 L s 1 g .10357 .21312 m .10357 .21312 .03171 0 365.73 arc F 0 g newpath .10357 .21312 .03171 0 365.73 arc s .89643 .21312 m .81714 .13383 L .97571 .13383 L .89643 .21312 L s .81714 .11798 m .97571 .11798 L s 1 g .89643 .21312 m .89643 .21312 .03171 0 365.73 arc F 0 g newpath .89643 .21312 .03171 0 365.73 arc s 1 0 0 r .5 Mabswid .89643 .21312 m .86427 .20309 L .82919 .19231 L .79624 .18248 L .76456 .17343 L .73084 .16438 L .69838 .15638 L .66387 .14878 L .63063 .14251 L .59865 .13757 L .58246 .13552 L .56463 .13364 L .54772 .13225 L .53187 .13131 L .52774 .13112 L .52323 .13095 L .51925 .13082 L .51502 .13071 L .51286 .13066 L .51082 .13062 L .50884 .13059 L .50702 .13057 L .50528 .13055 L .5044 .13055 L .50345 .13054 L .5025 .13054 L .50161 .13053 L .50056 .13053 L .49959 .13053 L .49861 .13053 L .49769 .13054 L .49668 .13054 L .49559 .13055 L .49451 .13055 L .49337 .13057 L .49134 .13059 L .48769 .13065 L .48371 .13074 L .47938 .13086 L .47475 .13102 L .46642 .13139 L .44865 .13252 L .43188 .13398 L .39985 .13777 L .36579 .14313 L .33298 .14943 L .30144 .15642 L .26786 .16472 L .23554 .1734 L .20118 .18323 L Mistroke .16808 .19314 L .13624 .20294 L .10357 .21312 L Mfstroke .68892 .19598 m .70751 .1167 L s .5 .17017 m .5 .09089 L s .31108 .19598 m .29249 .1167 L s 0 g 2 Mabswid .10357 .21312 m .02429 .13383 L .18286 .13383 L .10357 .21312 L s 1 g .10357 .21312 m .10357 .21312 .03171 0 365.73 arc F 0 g newpath .10357 .21312 .03171 0 365.73 arc s .89643 .21312 m .81714 .13383 L .97571 .13383 L .89643 .21312 L s .81714 .11798 m .97571 .11798 L s 1 g .89643 .21312 m .89643 .21312 .03171 0 365.73 arc F 0 g newpath .89643 .21312 .03171 0 365.73 arc s 0 0 m 1 0 L 1 .42624 L 0 .42624 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 122.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooR7>L00<007>LLi`0QG>L2Goo0007Oon7Li`30026Li`9Ool000Mo ohMcW0<008IcW0Uoo`001gooQW>L00D007>L001cW00008EcW0Uoo`001gooQW>L00D007>L001cW000 08EcW0Uoo`001gooQG>L00@007>LLi`0009cW003001cW7>L089cW0Uoo`001gooQG>L00@007>LLi`0 009cW003001cW7>L089cW0Uoo`001gooQ7>L00D007>LLiacW00000=cW003001cW7>L085cW0Uoo`00 1gooQ7>L00D007>LLiacW00000=cW003001cW7>L085cW0Uoo`001gooPg>L00<007>LLi`00W>L00<0 07>LLi`00W>L00<007>LLi`0P7>L2Goo0007Oon3Li`00`00LiacW002Li`00`00LiacW002Li`00`00 LiacW020Li`9Ool000Mooh9cW003001cW7>L00=cW003O01cW7>L00=cW003001cW7>L07mcW0Uoo`00 1gooPW>L00<007>LLi`00g>L00=l07>LLi`00g>L00<007>LLi`0Og>L2Goo0007Oon1Li`00`00Liac W004Li`00g`0LiacW004Li`00`00LiacW01nLi`9Ool000Mooh5cW003001cW7>L00AcW003O01cW7>L 00AcW003001cW7>L07icW0Uoo`001gooP7>L00<007>LLi`01G>L00=l07>LLi`01G>L00<007>LLi`0 OG>L2Goo0007Oon8Li`00g`0LiacW025Li`9Ool000MoohQcW003O01cW7>L08EcW0Uoo`001gooCG>L 00=l07>LLi`0>7>L00=l07>LLi`0>7>L00=l07>LLi`077>L;`0027oo0007Oom=Li`00g`0LiacW00h Li`00g`0LiacW00hLi`00g`0LiacW00LLi`_0008Ool000MoodecW003O01cW7>L03QcW003O01cW7>L 03QcW003O01cW7>L04YcW0Uoo`001gooCW>L00=l07>LLi`0=g>L00=l07>LLi`0=g>L00=l07>LLi`0 Bg>L2Goo0007Oom>Li`00g`0LiacW00[Li`HO00^Li`00g`0LiacW01;Li`9Ool000Iooc0001mcW003 O01cW7>L021cW0]l00acW003O01cW7>L00UcW0il021cW003O01cW7>L01ecW30000Moo`001goo;P00 87>L00=l07>LLi`067>L27`05g>L00=l07>LLi`05g>L1g`06G>L00=l07>LLi`07W>L;P0027oo0007 Ool017>L000000009W>L0`008W>L00=l07>LLi`04g>L17`07g>L00=l07>LLi`07W>L1g`04G>L00=l 07>LLi`087>L0`009W>L0`002Goo0007Ool2Li`3000TLi`3000SLi`00g`0LiacW00LOomoo`07Ool000Moo`=cW0<0 029cW0<002AcW003O01cW7>L00AcW0Ql02YcW003O01cW7>L02YcW0El00McW003O01cW7>L029cW0<0 029cW0<0009cW0Uoo`001goo17>L0`0087>L0`009G>L00=l07>LLi`017`0L00=l07>LLi`0;g>L 1G`00W>L00=l07>LLi`08g>L0`0087>L0`000g>L2Goo0007Ool5Li`3000NLi`3000ULi`4O00fLi`0 0g`0LiacW00dLi`4O00ULi`3000NLi`30004Li`9Ool000Moo`IcW0<001acW0<002=cW0=l009cW003 O01cW7>L03EcW003O01cW7>L03EcW003O01cW7>L00=l02=cW0<001acW0<000EcW0Uoo`001goo1g>L 0`006W>L0`008G>L0g`01G>L00=l07>LLi`0=G>L00=l07>LLi`0=G>L00=l07>LLi`00g>L0g`08G>L 0`006W>L0`001W>L2Goo0007Ool8Li`3000HLi`3000NLi`4O008Li`00g`0LiacW00eLi`00g`0Liac W00eLi`00g`0LiacW006Li`4O00NLi`3000HLi`30007Li`9Ool000Moo`UcW0<001IcW0<001YcW0El 00acW003O01cW7>L03EcW003O01cW7>L03EcW003O01cW7>L00YcW0El01YcW0<001IcW0<000QcW0Uo o`001goo2W>L0`005G>L0P005g>L17`047>L00<007`0Li`0=W>L00<007>LLi`0=G>L00=l0000Li`0 3g>L17`05g>L0P005G>L0`002G>L2Goo0007Ool;Li`3000CLi`2000ELi`3O00DLi`00`00Lial000f Li`00`00LiacW00dLi`00g`0Li`0000DLi`3O00ELi`2000CLi`3000:Li`9Ool000Moo`acW0<0015c W0<0019cW0=l01McW003001cW7`003IcW003001cW7>L03AcW003O01cW00001McW0=l019cW0<0015c W0<000]cW0Uoo`001goo3G>L0`000W>L2P000g>L0`0047>L0g`06W>L00<007>LO000=W>L00<007>L Li`0=7>L00=l07>L00006W>L0g`047>L0`000g>L2@000g>L0`0037>L2Goo0007Ool>Li`?000017>L 000000003W>L0g`07G>L00<007>LO00067>L00<007>LLi`06g>L00<007>LLi`0=7>L00=l07>L0000 7G>L0g`03W>L3`0000AcW000000000ecW0Uoo`001goo3g>L100027oo1@002g>L17`087>L00@007>L Lial01EcW08001icW003001cW7>L03=cW004O01cW7>L000PLi`3O00Li`9Ool0 00Mooa1cW08000Yoo`@000QcW0=l02AcW004001cW7>LO00CLi`2000PLi`00`00LiacW00cLi`017`0 LiacW0008g>L0g`02W>L0P002Woo10003W>L2Goo0007Ool?Li`2000=Ool20005Li`3O00WLi`01000 LiacW7`04G>L0P008W>L00<007>LLi`0L00Al07>LLi`002IcW0=l00IcW08000eoo`8000icW0Uo o`001goo3W>L0P003Woo0P000W>L0g`0:W>L00<007>LLi`047>L0P0097>L00<007>LLi`0=W>L00<0 07>LLi`09g>L17`000=cW00000003goo0P003G>L2Goo0007Ool=Li`3000?Ool00`00O01l000]Li`0 0`00LiacW00>Li`2000VLi`00`00LiacW00fLi`00`00LiacW00[Li`3000@Ool00`00LiacW00;Li`9 Ool000Moo`ecW080011oo`8002icW003001cW7>L00acW08002QcW003001cW7>L03IcW003001cW7>L 02]cW080011oo`8000ecW0Uoo`001goo3G>L0P004Goo00<007>LLi`0;7>L00<007>LLi`02W>L0P00 :W>L00<007>LLi`0=W>L00<007>LLi`0:g>L0P0047oo0P003G>L2Goo0007Ool=Li`2000@OooB000@ Ool2000=Li`9Ool000Moo`ecW080011oom80011oo`8000ecW0Uoo`001goo3G>L0P0047oo0P00;W>L 00<007>LLi`03G>L0P009g>L00<007>LLi`0=W>L00<007>LLi`0;7>L0P003goo0P003G>L2Goo0007 Ool=Li`3000?Ool00`00LiacW00]Li`00`00LiacW00?Li`2000ULi`00`00LiacW00fLi`00`00Liac W00]Li`2000>Ool2000=Li`9Ool000Moo`icW08000ioo`8002mcW003001cW7>L015cW08002=cW003 001cW7>L03IcW003001cW7>L02ecW08000ioo`8000ecW0Uoo`001goo3g>L0P0037oo0P00<7>L00<0 07>LLi`04g>L0P008G>L00<007>LLi`0=W>L00<007>LLi`0;W>L0P0037oo0P003W>L2Goo0007Ool@ Li`2000:Ool2000aLi`00`00LiacW00ELi`2000OLi`00`00LiacW00fLi`00`00LiacW00_Li`20009 Ool3000?Li`9Ool000Mooa1cW0@000Ioo`@0035cW003001cW7>L01McW08001ecW003001cW7>L03Ic W003001cW7>L02mcW0@000Ioo`@000mcW0Uoo`001goo4G>L3000L00<007>LLi`0=W>L00<007>L Li`0=W>L00<007>LLi`0<7>L1P0000=oo`0000000P004G>L2Goo0007OolCLi`8000dLi`00`00Liac W00fLi`00`00LiacW00fLi`00`00LiacW00bLi`8000BLi`9Ool000MooaMcW08003IcW003001cW7>L 03IcW003001cW7>L03IcW003001cW7>L03EcW0<001AcW0Uoo`001gooCg>L00<007>LLi`0=W>L00<0 07>LLi`0=W>L00<007>LLi`0C7>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`@Li`00`00Oomoo`07Ool000MooomcW11cW003001oogoo00Moo`00ogoo8Goo003oOolQOol00001 \ \>"], ImageRangeCache->{{{0, 287}, {121.75, 0}} -> {-1.13365, -0.268802, \ 0.00441565, 0.00441565}}] }, Open ]] }, Open ]] }, Closed]], 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[ \(\(scQ = 0.01;\)\)], "Input"], Cell[BoxData[ \(\(scM = 0.02;\)\)], "Input"] }, Closed]], 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: .42624 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 0.896429 0.792858 0.21312 0.792858 [ [ 0 0 0 0 ] [ 1 .42624 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .01015 m .02381 .41609 L .97619 .41609 L .97619 .01015 L F 0 g 2 Mabswid [ ] 0 setdash .89643 .21312 m .10357 .21312 L s 0 1 .4 r .5 Mabswid .89643 .21312 m .86427 .21312 L .82919 .21312 L .79624 .21312 L .76456 .21312 L .73084 .21312 L .69838 .21312 L .66387 .21312 L .63063 .21312 L .59865 .21312 L .56463 .21312 L .53187 .21312 L .50037 .21312 L .46683 .21312 L .43456 .21312 L .40024 .21312 L .36718 .21312 L .33538 .21312 L .30155 .21312 L .26897 .21312 L .23435 .21312 L .201 .21312 L .1689 .21312 L .13477 .21312 L .10357 .21312 L s .89643 .21312 m .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L s .10357 .21312 m .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L s 0 0 m 1 0 L 1 .42624 L 0 .42624 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 122.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001goo5g>L00<3k7>LLi`0gg>L00<3k7>LLi`057>L2Goo0007 OolFLi`00`000n`3k03Q0n`FLi`9Ool000MooaIcW>@001IcW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 ogoo8Goo003oOolQOol00001\ \>"], ImageRangeCache->{{{0, 287}, {121.75, 0}} -> {-1.13365, -0.268802, \ 0.00441565, 0.00441565}}] }, 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: .42624 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 0.896429 0.792858 0.21312 0.792858 [ [ 0 0 0 0 ] [ 1 .42624 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .01015 m .02381 .41609 L .97619 .41609 L .97619 .01015 L F 0 g 2 Mabswid [ ] 0 setdash .89643 .21312 m .10357 .21312 L s 0 .4 1 r .5 Mabswid .89643 .41133 m .86427 .41133 L .82919 .41133 L .79624 .41133 L .76456 .41133 L .73084 .41133 L .69838 .41133 L .66387 .41133 L .63063 .41133 L .59865 .41133 L .56463 .41133 L .53187 .41133 L .51542 .41133 L .50823 .41133 L .50443 .41133 L .50234 .41133 L .50132 .41133 L .50037 .41133 L .49929 .01491 L .49872 .01491 L .49812 .01491 L .49608 .01491 L .49209 .01491 L .48422 .01491 L .46683 .01491 L .43522 .01491 L .40157 .01491 L .36918 .01491 L .33474 .01491 L .30157 .01491 L .26966 .01491 L .23571 .01491 L .20302 .01491 L .1716 .01491 L .13813 .01491 L .10592 .01491 L .10357 .01491 L s .89643 .21312 m .89643 .22116 L .89643 .22993 L .89643 .23817 L .89643 .24609 L .89643 .25452 L .89643 .26263 L .89643 .27126 L .89643 .27957 L .89643 .28756 L .89643 .29607 L .89643 .30426 L .89643 .31213 L .89643 .32052 L .89643 .32859 L .89643 .33717 L .89643 .34543 L .89643 .35338 L .89643 .36184 L .89643 .36998 L .89643 .37864 L .89643 .38698 L .89643 .395 L .89643 .40354 L .89643 .41133 L s .10357 .21312 m .10357 .20508 L .10357 .19631 L .10357 .18807 L .10357 .18015 L .10357 .17172 L .10357 .16361 L .10357 .15498 L .10357 .14667 L .10357 .13868 L .10357 .13017 L .10357 .12198 L .10357 .11411 L .10357 .10572 L .10357 .09765 L .10357 .08907 L .10357 .08081 L .10357 .07286 L .10357 .0644 L .10357 .05626 L .10357 .0476 L .10357 .03926 L .10357 .03124 L .10357 .02271 L .10357 .01491 L s .86471 .32808 m .86471 .3268 L .86471 .32539 L .86471 .32408 L .86471 .32281 L .86471 .32146 L .86471 .32016 L .86471 .31878 L .86471 .31745 L .86471 .31617 L .86471 .31481 L .86471 .3135 L .86471 .31224 L .86471 .3109 L .86471 .30961 L .86471 .30824 L .86471 .30691 L .86471 .30564 L .86471 .30429 L .86471 .30299 L .86471 .3016 L .86471 .30027 L .86471 .29898 L .86471 .29762 L .86471 .29637 L s .15114 .11401 m .14986 .11401 L .14845 .11401 L .14714 .11401 L .14587 .11401 L .14452 .11401 L .14322 .11401 L .14184 .11401 L .14051 .11401 L .13923 .11401 L .13787 .11401 L .13656 .11401 L .1353 .11401 L .13396 .11401 L .13267 .11401 L .13129 .11401 L .12997 .11401 L .1287 .11401 L .12735 .11401 L .12604 .11401 L .12466 .11401 L .12333 .11401 L .12204 .11401 L .12068 .11401 L .11943 .11401 L s .88057 .31223 m .87929 .31223 L .87788 .31223 L .87656 .31223 L .8753 .31223 L .87395 .31223 L .87265 .31223 L .87127 .31223 L .86994 .31223 L .86866 .31223 L .8673 .31223 L .86599 .31223 L .86473 .31223 L .86339 .31223 L .8621 .31223 L .86072 .31223 L .8594 .31223 L .85813 .31223 L .85678 .31223 L .85547 .31223 L .85409 .31223 L .85275 .31223 L .85147 .31223 L .85011 .31223 L .84886 .31223 L s 0 0 m 1 0 L 1 .42624 L 0 .42624 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 122.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL06icW0030Imc W7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiac W01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo 5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025 Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L 00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW003 0ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo 0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030Imc W7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiac W01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo 5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025 Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L 00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW003 0ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo 0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030Imc W7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiac W01^Li`00`6OLiacW025Li`9Ool000MooaMcW0040ImcW7>LLi`:0ImSLi`00`6OLiacW025Li`9Ool0 00MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>L Li`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L 06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolG Li`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08Ec W0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`0 0`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1 Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool0 00MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>L Li`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L 06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolG Li`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08Ec W0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`0 0`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1 Wg>LLi`0KW>L00<1Wg>LLi`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool0 00MooaMcW0030ImcW7>L06icW0030ImcW7>L08EcW0Uoo`001goo5g>L00<1Wg>LLi`0KW>L00<1Wg>L Li`0QG>L2Goo0007OolGLi`00`6OLiacW01^Li`00`6OLiacW025Li`9Ool000MooaMcW0030ImcW7>L 06icW0030ImcW7>L08EcW0Uoo`001goo5W>L00<0006O0000K`0000<1W`000000KP0000<1Wg>LLi`0 57>L2Goo0007OolFLiab00000`6O0000001^00000`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L 06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8 Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01Ac W0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`0 0`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1 Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool0 00MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>L Li`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L 06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8 Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01Ac W0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`0 0`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1 Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool0 00MoohQcW0030ImcW7>L06EcW0030ImcW7>L00IcW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>L Li`0IG>L00<1Wg>LLi`01W>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01ULi`00`6OLiac W006Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06EcW0030ImcW7>L00IcW0030ImcW7>L 01AcW0Uoo`001gooR7>L00<1Wg>LLi`0IG>L00<1Wg>LLi`01W>L00<1Wg>LLi`057>L2Goo0007Oon8 Li`00`6OLiacW01QLi`:0Il3Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06EcW0030Imc W7>L00IcW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0IG>L00<1Wg>LLi`01W>L00<1Wg>L Li`057>L2Goo0007Oon8Li`00`6OLiacW01ULi`00`6OLiacW006Li`00`6OLiacW00DLi`9Ool000Mo ohQcW0030ImcW7>L06EcW0030ImcW7>L00IcW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0 KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQc W0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L 2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW003 0ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6O LiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`00 1gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiac W00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0 KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQc W0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L 2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW003 0ImcW7>L01AcW0Uoo`001gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6O LiacW01^Li`00`6OLiacW00DLi`9Ool000MoohQcW0030ImcW7>L06icW0030ImcW7>L01AcW0Uoo`00 1gooR7>L00<1Wg>LLi`0KW>L00<1Wg>LLi`057>L2Goo0007Oon8Li`00`6OLiacW01^Li`00`6OLiac W00DLi`9Ool000MoohQcW781WaIcW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool00?moob5o o`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {121.75, 0}} -> {-1.13365, -0.268802, \ 0.00441565, 0.00441565}}] }, 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: .42624 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 0.896429 0.792858 0.21312 0.792858 [ [ 0 0 0 0 ] [ 1 .42624 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath .9 g .02381 .01015 m .02381 .41609 L .97619 .41609 L .97619 .01015 L F 0 g 2 Mabswid [ ] 0 setdash .89643 .21312 m .10357 .21312 L s .8 0 1 r .5 Mabswid .89643 .21312 m .86427 .19704 L .82919 .1795 L .79624 .16303 L .76456 .14719 L .73084 .13032 L .69838 .11409 L .66387 .09684 L .63063 .08022 L .59865 .06423 L .56463 .04722 L .53187 .03084 L .51542 .02262 L .50823 .01902 L .50443 .01712 L .50234 .01608 L .50132 .01556 L .50037 .01509 L .49929 .01526 L .49872 .01554 L .49812 .01585 L .49608 .01687 L .49209 .01886 L .48422 .0228 L .46683 .03149 L .43522 .04729 L .40157 .06412 L .36918 .08032 L .33474 .09753 L .30157 .11412 L .26966 .13007 L .23571 .14705 L .20302 .16339 L .1716 .17911 L .13813 .19584 L .10592 .21195 L .10357 .21312 L s .89643 .21312 m .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L .89643 .21312 L s .10357 .21312 m .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L .10357 .21312 L s 0 0 m 1 0 L 1 .42624 L 0 .42624 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 122.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgL0V@O1W>L0V@OPg>L2Goo0007Oon2Li`00f@OLiacW008Li`2I1n1Li`9Ool000Mooh1c W09T7`ecW09T7gmcW0Uoo`001gooOW>L0V@O4G>L0V@OOG>L2Goo0007OomlLi`2I1lELi`2I1mkLi`9 Ool000MoogUcW0=T7aUcW09T7gUcW0Uoo`001gooMg>L0V@O7W>L0V@OMg>L2Goo0007OomeLi`2I1lR Li`2I1meLi`9Ool000Moog=cW09T7bIcW09T7g=cW0Uoo`001gooLG>L0V@O:W>L0V@OLG>L2Goo0007 Oom_Li`2I1l^Li`2I1m_Li`9Ool000MoofecW09T7c9cW09T7fecW0Uoo`001gooK7>L00=T7g>LLi`0 =7>L0V@OJg>L2Goo0007OomZLi`2I1liLi`2I1mYLi`9Ool000MoofQcW09T7cecW09T7fMcW0Uoo`00 1gooIW>L0V@O@G>L0V@OIG>L2Goo0007OomTLi`2I1m5Li`2I1mSLi`9Ool000Moof=cW003I1mcW7>L 04McW09T7f5cW0Uoo`001gooHG>L0V@OC7>L0V@OGg>L2Goo0007OomOLi`2I1m@Li`3I1mLLi`9Ool0 00MooeecW09T7eEcW09T7eYcW0Uoo`001gooFg>L0V@OFG>L0V@OF7>L2Goo0007OomHLi`3I1mMLi`2 I1mFLi`9Ool000MooeIcW09T7f9cW09T7eAcW0Uoo`001gooDg>L0f@OIW>L0V@ODW>L2Goo0007OomA Li`2I1m[Li`2I1m@Li`9Ool000MoodmcW09T7fmcW09T7dicW0Uoo`001gooCG>L0V@OLg>L0V@OC7>L 2Goo0007Oom;Li`2I1mgLi`2I1m:Li`9Ool000MoodUcW09T7g]cW09T7dQcW0Uoo`001gooAg>L0V@O Og>L0V@OAW>L2Goo0007Oom6Li`00f@OLiacW021Li`00f@OLiacW013Li`9Ool000MoodAcW09T7hEc W09T7d=cW0Uoo`001goo@W>L0V@ORG>L0V@O@G>L2Goo0007Oom0Li`2I1n=Li`2I1loLi`9Ool000Mo ocicW09T7i5cW09T7cecW0Uoo`001goo?7>L0V@OUG>L0f@O>W>L2Goo0007OoljLi`2I1nJLi`2I1lh Li`9Ool000MoocMcW0=T7iicW09T7cIcW0Uoo`001goo=G>L0V@OXg>L0V@O=7>L2Goo0007OolcLi`2 I1nWLi`2I1lbLi`9Ool000Mooc5cW09T7j]cW09T7c1cW0Uoo`001goo;g>L0V@O[g>L0V@O;W>L2Goo 0007Ool]Li`2I1ncLi`2I1l/Li`9Ool000Moob]cW09T7kMcW09T7bYcW0Uoo`001goo:W>L00=T7g>L Li`0^G>L00=T7g>LLi`09g>L2Goo0007OolXLi`2I1nmLi`2I1lWLi`9Ool000MoobIcW09T7l5cW09T 7bEcW0Uoo`001goo97>L0V@OaG>L0V@O8g>L2Goo0007OolRLi`2I1o9Li`2I1lQLi`9Ool000Moob1c W09T7lecW09T7amcW0Uoo`001goo7W>L0V@OdG>L0V@O7G>L2Goo0007OolKLi`3I1oELi`2I1lKLi`9 Ool000MooaUcW09T7mYcW09T7aUcW0Uoo`001goo5g>L0V@OgW>L0f@O5W>L2Goo0007OolFLi`00`00 I1l0003P00000f@OLiacW00DLi`9Ool000MooaIcW>@001IcW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 1gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007Oooo Li`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15c W0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo 0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000Mo oomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L 4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9 Ool000MooomcW15cW0Uoo`001gooog>L4G>L2Goo0007OoooLi`ALi`9Ool000MooomcW15cW0Uoo`00 ogoo8Goo003oOolQOol00001\ \>"], ImageRangeCache->{{{0, 287}, {121.75, 0}} -> {-1.13365, -0.268802, \ 0.00441565, 0.00441565}}] }, 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[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-06a\\outmath"\)], "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[ \({120, 51}\)], "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[ \("C:\\Wrk\\Corsi\\Scost\\esercizi\\7-travi\\7-06a\\outmath"\)], "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 = simplifyDirac[\[Zeta], 0, L[i]]\)} }, 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$\"\>", "\<\"g$1199\"\>"}, {"\<\"g$1264\"\>", "\<\"g$2472\"\>", "\<\"g$2537\"\>", \ "\<\"g$2634\"\>", "\<\"g$2664\"\>", "\<\"g$2904\"\>"}, {"\<\"g$307\"\>", "\<\"g$3270\"\>", "\<\"g$3505\"\>", \ "\<\"g$372\"\>", "\<\"g$3846\"\>", "\<\"g$4040\"\>"}, {"\<\"g$4429\"\>", "\<\"g$475\"\>", "\<\"g$665\"\>", "\<\"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$", "g$1199"}, { "g$1264", "g$2472", "g$2537", "g$2634", "g$2664", "g$2904"}, {"g$307", "g$3270", "g$3505", "g$372", "g$3846", "g$4040"}, {"g$4429", "g$475", "g$665", "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->{640, 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, 30, "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, 116, 3, 46, "Input"], Cell[8564, 271, 319, 9, 60, "SmallText"], Cell[8886, 282, 116, 3, 46, "Input"], Cell[9005, 287, 215, 5, 66, "Input"], Cell[9223, 294, 130, 3, 28, "SmallText"], Cell[9356, 299, 129, 3, 46, "Input"], Cell[9488, 304, 121, 3, 28, "SmallText"], Cell[9612, 309, 199, 5, 58, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[9848, 319, 56, 0, 31, "Subsection"], Cell[9907, 321, 45, 0, 28, "SmallText"], Cell[9955, 323, 124, 3, 30, "Input"], Cell[10082, 328, 42, 0, 28, "SmallText"], Cell[10127, 330, 118, 2, 30, "Input"], Cell[10248, 334, 43, 1, 30, "Input"], Cell[10294, 337, 227, 4, 28, "SmallText"], Cell[10524, 343, 53, 1, 30, "Input"], Cell[10580, 346, 271, 5, 42, "Input"], Cell[10854, 353, 46, 0, 28, "SmallText"], Cell[10903, 355, 195, 4, 42, "Input"], Cell[11101, 361, 52, 0, 28, "SmallText"], Cell[11156, 363, 504, 9, 131, "Input"], Cell[11663, 374, 613, 11, 131, "Input"], Cell[12279, 387, 73, 0, 28, "SmallText"], Cell[12355, 389, 46, 1, 30, "Input"], Cell[12404, 392, 134, 3, 28, "SmallText"], Cell[12541, 397, 182, 4, 30, "Input"], Cell[12726, 403, 146, 3, 30, "Input"], Cell[12875, 408, 42, 0, 28, "SmallText"], Cell[12920, 410, 203, 4, 42, "Input"], Cell[13126, 416, 48, 0, 28, "SmallText"], Cell[13177, 418, 226, 5, 85, "Input"], Cell[13406, 425, 205, 5, 42, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[13648, 435, 111, 3, 50, "Subsection"], Cell[CellGroupData[{ Cell[13784, 442, 144, 2, 70, "Input"], Cell[13931, 446, 3815, 112, 80, 948, 72, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[17807, 565, 150, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[17982, 575, 103, 5, 47, "Subsection"], Cell[18088, 582, 62, 1, 30, "Input"], Cell[18153, 585, 57, 1, 30, "Input"], Cell[18213, 588, 417, 11, 76, "SmallText"], Cell[18633, 601, 192, 5, 58, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[18862, 611, 210, 7, 66, "Subsection"], Cell[CellGroupData[{ Cell[19097, 622, 52, 1, 30, "Input"], Cell[19152, 625, 46, 1, 70, "Output"] }, Open ]], Cell[19213, 629, 310, 5, 116, "Input"], Cell[CellGroupData[{ Cell[19548, 638, 50, 1, 30, "Input"], Cell[19601, 641, 46, 1, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[19708, 649, 116, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[19849, 656, 132, 3, 66, "Subsection"], Cell[19984, 661, 137, 3, 30, "Input"], Cell[20124, 666, 74, 1, 30, "Input"], Cell[20201, 669, 1102, 28, 50, "Input"], Cell[CellGroupData[{ Cell[21328, 701, 92, 1, 30, "Input"], Cell[21423, 704, 55, 1, 70, "Output"] }, Open ]], Cell[21493, 708, 105, 2, 30, "Input"], Cell[CellGroupData[{ Cell[21623, 714, 174, 3, 30, "Input"], Cell[21800, 719, 611, 11, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[22460, 736, 64, 0, 31, "Subsection"], Cell[22527, 738, 280, 6, 44, "SmallText"], Cell[CellGroupData[{ Cell[22832, 748, 87, 1, 30, "Input"], Cell[22922, 751, 109, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23068, 758, 104, 2, 30, "Input"], Cell[23175, 762, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23270, 768, 190, 3, 50, "Input"], Cell[23463, 773, 152, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23652, 780, 264, 4, 71, "Input"], Cell[23919, 786, 183, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24139, 794, 65, 1, 30, "Input"], Cell[24207, 797, 605, 11, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[24861, 814, 66, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[24952, 818, 116, 2, 30, "Input"], Cell[25071, 822, 1464, 44, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26572, 871, 290, 5, 50, "Input"], Cell[26865, 878, 1560, 42, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[28462, 925, 289, 5, 50, "Input"], Cell[28754, 932, 1319, 39, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[30134, 978, 62, 0, 39, "Section"], Cell[30199, 980, 71, 1, 30, "Input"], Cell[30273, 983, 146, 3, 28, "SmallText"], Cell[30422, 988, 408, 9, 70, "Input"], Cell[30833, 999, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[30928, 1003, 198, 4, 50, "Input"], Cell[31129, 1009, 174, 3, 70, "Output"] }, Open ]], Cell[31318, 1015, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[31413, 1019, 198, 4, 50, "Input"], Cell[31614, 1025, 174, 3, 70, "Output"] }, Open ]], Cell[31803, 1031, 64, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[31892, 1035, 190, 4, 50, "Input"], Cell[32085, 1041, 151, 2, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[32285, 1049, 128, 5, 39, "Section"], Cell[CellGroupData[{ Cell[32438, 1058, 53, 0, 47, "Subsection"], Cell[32494, 1060, 110, 2, 30, "Input"], Cell[32607, 1064, 152, 3, 30, "Input"], Cell[32762, 1069, 249, 5, 50, "Input"], Cell[33014, 1076, 330, 6, 70, "Input"], Cell[33347, 1084, 193, 4, 30, "Input"], Cell[33543, 1090, 133, 3, 28, "SmallText"] }, Closed]], Cell[CellGroupData[{ Cell[33713, 1098, 103, 5, 31, "Subsection"], Cell[33819, 1105, 160, 4, 60, "SmallText"], Cell[33982, 1111, 49, 1, 30, "Input"], Cell[34034, 1114, 106, 2, 50, "Input"], Cell[34143, 1118, 119, 3, 28, "SmallText"], Cell[34265, 1123, 80, 2, 46, "Input"], Cell[34348, 1127, 505, 8, 92, "SmallText"], Cell[34856, 1137, 165, 4, 46, "Input"], Cell[35024, 1143, 224, 3, 110, "Input"], Cell[CellGroupData[{ Cell[35273, 1150, 40, 1, 30, "Input"], Cell[35316, 1153, 115, 2, 70, "Output"] }, Open ]], Cell[35446, 1158, 70, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[35541, 1162, 137, 3, 30, "Input"], Cell[35681, 1167, 130, 2, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[35860, 1175, 56, 0, 31, "Subsection"], Cell[35919, 1177, 72, 0, 28, "SmallText"], Cell[35994, 1179, 44, 1, 30, "Input"], Cell[CellGroupData[{ Cell[36063, 1184, 43, 1, 30, "Input"], Cell[36109, 1187, 78, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36224, 1193, 280, 5, 90, "Input"], Cell[36507, 1200, 36, 1, 70, "Output"] }, Open ]], Cell[36558, 1204, 150, 3, 44, "SmallText"], Cell[36711, 1209, 43, 1, 30, "Input"], Cell[36757, 1212, 53, 1, 30, "Input"], Cell[36813, 1215, 1277, 26, 270, "Input"], Cell[CellGroupData[{ Cell[38115, 1245, 240, 4, 70, "Input"], Cell[38358, 1251, 36, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38431, 1257, 48, 1, 30, "Input"], Cell[38482, 1260, 396, 12, 70, "Output"] }, Open ]], Cell[38893, 1275, 90, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[39008, 1281, 43, 1, 30, "Input"], Cell[39054, 1284, 78, 1, 70, "Output"] }, Open ]], Cell[39147, 1288, 222, 4, 90, "Input"], Cell[39372, 1294, 219, 4, 90, "Input"], Cell[39594, 1300, 67, 0, 28, "SmallText"], Cell[39664, 1302, 72, 1, 30, "Input"], Cell[39739, 1305, 82, 1, 30, "Input"], Cell[39824, 1308, 393, 7, 208, "Input"], Cell[40220, 1317, 403, 7, 208, "Input"], Cell[40626, 1326, 214, 4, 118, "Input"], Cell[40843, 1332, 717, 13, 338, "Input"], Cell[41563, 1347, 452, 8, 202, "Input"], Cell[42018, 1357, 213, 4, 90, "Input"], Cell[42234, 1363, 155, 3, 70, "Input"], Cell[42392, 1368, 57, 1, 30, "Input"], Cell[42452, 1371, 59, 1, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[42548, 1377, 75, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[42648, 1381, 145, 2, 70, "Input"], Cell[42796, 1385, 5567, 141, 89, 1075, 81, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[48400, 1531, 144, 2, 70, "Input"], Cell[48547, 1535, 3834, 128, 66, 1212, 91, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[52430, 1669, 78, 0, 47, "Subsection"], Cell[52511, 1671, 231, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[52767, 1679, 213, 4, 50, "Input"], Cell[52983, 1685, 902, 27, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[53922, 1717, 70, 1, 30, "Input"], Cell[53995, 1720, 490, 15, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[54546, 1742, 89, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[54660, 1747, 68, 1, 47, "Subsection", Evaluatable->False], Cell[54731, 1750, 119, 3, 28, "SmallText"], Cell[54853, 1755, 156, 3, 28, "SmallText"], Cell[55012, 1760, 356, 5, 95, "Input"], Cell[55371, 1767, 343, 6, 115, "Input"], Cell[CellGroupData[{ Cell[55739, 1777, 37, 1, 30, "Input"], Cell[55779, 1780, 311, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[56127, 1790, 71, 1, 30, "Input"], Cell[56201, 1793, 551, 9, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[56801, 1808, 57, 0, 31, "Subsection"], Cell[56861, 1810, 94, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[56980, 1816, 169, 3, 30, "Input"], Cell[57152, 1821, 115, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[57304, 1828, 93, 1, 30, "Input"], Cell[57400, 1831, 115, 2, 70, "Output"] }, Open ]], Cell[57530, 1836, 61, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[57616, 1840, 344, 6, 90, "Input"], Cell[57963, 1848, 130, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[58130, 1855, 69, 1, 30, "Input"], Cell[58202, 1858, 108, 2, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[58359, 1866, 65, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[58449, 1870, 70, 1, 30, "Input"], Cell[58522, 1873, 282, 5, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[58853, 1884, 105, 2, 50, "Subsection"], Cell[CellGroupData[{ Cell[58983, 1890, 195, 4, 30, "Input"], Cell[59181, 1896, 184, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[59402, 1904, 63, 1, 30, "Input"], Cell[59468, 1907, 219, 4, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[59736, 1917, 88, 1, 31, "Subsection", Evaluatable->False], Cell[59827, 1920, 180, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[60032, 1928, 37, 1, 30, "Input"], Cell[60072, 1931, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[60167, 1937, 138, 4, 30, "Input"], Cell[60308, 1943, 58, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[60403, 1949, 103, 2, 30, "Input"], Cell[60509, 1953, 234, 4, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[60780, 1962, 134, 3, 30, "Input"], Cell[60917, 1967, 288, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[61242, 1980, 134, 3, 30, "Input"], Cell[61379, 1985, 583, 18, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[62011, 2009, 78, 0, 31, "Subsection"], Cell[62092, 2011, 83, 1, 28, "SmallText"], Cell[CellGroupData[{ Cell[62200, 2016, 45, 1, 30, "Input"], Cell[62248, 2019, 35, 1, 70, "Output"] }, Open ]], Cell[62298, 2023, 218, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[62541, 2031, 51, 1, 30, "Input"], Cell[62595, 2034, 35, 1, 70, "Output"] }, Open ]], Cell[62645, 2038, 123, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[62793, 2045, 53, 1, 30, "Input"], Cell[62849, 2048, 35, 1, 70, "Output"] }, Open ]], Cell[62899, 2052, 132, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[63056, 2059, 51, 1, 30, "Input"], Cell[63110, 2062, 35, 1, 70, "Output"] }, Open ]], Cell[63160, 2066, 30, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[63215, 2070, 134, 2, 30, "Input"], Cell[63352, 2074, 52, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[63441, 2080, 230, 5, 30, "Input"], Cell[63674, 2087, 35, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[63758, 2094, 72, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[63855, 2098, 461, 8, 19, "Input", CellOpen->False], Cell[64319, 2108, 195, 5, 121, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[64551, 2118, 1993, 32, 19, "Input", CellOpen->False], Cell[66547, 2152, 186, 5, 66, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[66794, 2164, 142, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[66961, 2174, 56, 0, 47, "Subsection"], Cell[67020, 2176, 75, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[67120, 2180, 92, 1, 50, "Input"], Cell[67215, 2183, 172, 3, 70, "Output"] }, Open ]], Cell[67402, 2189, 182, 3, 44, "SmallText"], Cell[67587, 2194, 248, 7, 50, "Input"], Cell[CellGroupData[{ Cell[67860, 2205, 71, 1, 30, "Input"], Cell[67934, 2208, 373, 12, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[68356, 2226, 134, 5, 31, "Subsection"], Cell[68493, 2233, 420, 7, 76, "SmallText"], Cell[68916, 2242, 104, 3, 46, "Input"], Cell[69023, 2247, 313, 9, 44, "SmallText"], Cell[69339, 2258, 407, 8, 106, "Input"], Cell[69749, 2268, 90, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[69864, 2274, 135, 3, 30, "Input"], Cell[70002, 2279, 36, 1, 70, "Output"] }, Open ]], Cell[70053, 2283, 127, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[70205, 2290, 140, 3, 70, "Input"], Cell[70348, 2295, 85, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[70470, 2301, 182, 4, 50, "Input"], Cell[70655, 2307, 124, 2, 70, "Output"] }, Open ]], Cell[70794, 2312, 46, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[70865, 2316, 46, 1, 30, "Input"], Cell[70914, 2319, 43, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[71006, 2326, 72, 0, 31, "Subsection"], Cell[71081, 2328, 141, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[71247, 2335, 271, 7, 50, "Input"], Cell[71521, 2344, 45, 1, 70, "Output"] }, Open ]], Cell[71581, 2348, 185, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[71791, 2356, 160, 4, 30, "Input"], Cell[71954, 2362, 36, 1, 70, "Output"] }, Open ]], Cell[72005, 2366, 524, 9, 110, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[72578, 2381, 88, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[72691, 2386, 52, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[72768, 2390, 76, 1, 30, "Input"], Cell[72847, 2393, 165, 4, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[73061, 2403, 91, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[73177, 2408, 571, 10, 70, "Input"], Cell[73751, 2420, 107, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[73895, 2427, 149, 2, 30, "Input"], Cell[74047, 2431, 280, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[74364, 2441, 40, 1, 30, "Input"], Cell[74407, 2444, 107, 2, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[74575, 2453, 116, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[74716, 2460, 45, 0, 47, "Subsection"], Cell[74764, 2462, 141, 3, 30, "Input"], Cell[CellGroupData[{ Cell[74930, 2469, 1094, 25, 50, "Input"], Cell[76027, 2496, 1015, 24, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[77091, 2526, 65, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[77181, 2530, 217, 4, 50, "Input"], Cell[77401, 2536, 186, 3, 70, "Output"] }, Open ]], Cell[77602, 2542, 79, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[77706, 2546, 365, 9, 30, "Input"], Cell[78074, 2557, 320, 8, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[78443, 2571, 40, 0, 31, "Subsection"], Cell[78486, 2573, 142, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[78653, 2580, 227, 3, 50, "Input"], Cell[78883, 2585, 397, 7, 70, "Output"] }, Open ]], Cell[79295, 2595, 108, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[79428, 2602, 289, 4, 70, "Input"], Cell[79720, 2608, 833, 18, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[80590, 2631, 246, 4, 70, "Input"], Cell[80839, 2637, 979, 15, 70, "Output"] }, Open ]], Cell[81833, 2655, 102, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[81960, 2661, 330, 5, 70, "Input"], Cell[82293, 2668, 818, 18, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[83148, 2691, 244, 4, 70, "Input"], Cell[83395, 2697, 816, 13, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84248, 2715, 169, 3, 30, "Input"], Cell[84420, 2720, 115, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[84572, 2727, 76, 1, 30, "Input"], Cell[84651, 2730, 1433, 23, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[86121, 2758, 75, 1, 30, "Input"], Cell[86199, 2761, 1193, 20, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[87441, 2787, 64, 0, 31, "Subsection"], Cell[87508, 2789, 225, 5, 44, "SmallText"], Cell[CellGroupData[{ Cell[87758, 2798, 190, 4, 50, "Input"], Cell[87951, 2804, 109, 2, 70, "Output"] }, Open ]], Cell[88075, 2809, 112, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[88212, 2816, 311, 7, 90, "Input"], Cell[88526, 2825, 109, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[88672, 2832, 257, 4, 50, "Input"], Cell[88932, 2838, 149, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89118, 2845, 127, 2, 31, "Input"], Cell[89248, 2849, 164, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89449, 2856, 60, 1, 30, "Input"], Cell[89512, 2859, 68, 1, 70, "Output"] }, Open ]], Cell[89595, 2863, 108, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[89728, 2870, 61, 1, 30, "Input"], Cell[89792, 2873, 945, 15, 70, "Output"] }, Open ]], Cell[90752, 2891, 102, 2, 28, "SmallText"], Cell[CellGroupData[{ Cell[90879, 2897, 59, 1, 30, "Input"], Cell[90941, 2900, 782, 13, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[91784, 2920, 78, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[91887, 2925, 64, 1, 47, "Subsection", Evaluatable->False], Cell[91954, 2928, 151, 3, 28, "SmallText"], Cell[CellGroupData[{ Cell[92130, 2935, 422, 8, 90, "Input"], Cell[92555, 2945, 138, 2, 70, "Output"] }, Open ]], Cell[92708, 2950, 191, 4, 28, "SmallText"], Cell[CellGroupData[{ Cell[92924, 2958, 82, 1, 30, "Input"], Cell[93009, 2961, 214, 4, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[93272, 2971, 78, 1, 31, "Subsection", Evaluatable->False], Cell[93353, 2974, 108, 2, 30, "Input"], Cell[CellGroupData[{ Cell[93486, 2980, 93, 1, 30, "Input"], Cell[93582, 2983, 282, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[93901, 2996, 93, 1, 30, "Input"], Cell[93997, 2999, 488, 14, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94522, 3018, 107, 2, 30, "Input"], Cell[94632, 3022, 35, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94704, 3028, 108, 2, 30, "Input"], Cell[94815, 3032, 36, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[94888, 3038, 39, 1, 30, "Input"], Cell[94930, 3041, 68, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[95047, 3048, 55, 0, 31, "Subsection"], Cell[95105, 3050, 246, 4, 70, "Input"], Cell[95354, 3056, 244, 4, 70, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[95635, 3065, 80, 1, 47, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[95740, 3070, 169, 3, 30, "Input"], Cell[95912, 3075, 131, 3, 70, "Output"] }, Open ]], Cell[96058, 3081, 42, 1, 30, "Input"], Cell[96103, 3084, 86, 1, 30, "Input"], Cell[CellGroupData[{ Cell[96214, 3089, 88, 1, 30, "Input"], Cell[96305, 3092, 131, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[96473, 3100, 221, 4, 30, "Input"], Cell[96697, 3106, 206, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[96940, 3116, 128, 2, 30, "Input"], Cell[97071, 3120, 3784, 93, 70, "Output"] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[100916, 3220, 123, 3, 66, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[101064, 3227, 140, 5, 47, "Subsection"], Cell[101207, 3234, 110, 2, 30, "Input"], Cell[101320, 3238, 78, 1, 30, "Input"], Cell[101401, 3241, 76, 1, 30, "Input"], Cell[101480, 3244, 59, 1, 30, "Input"], Cell[101542, 3247, 471, 8, 139, "Input"], Cell[102016, 3257, 65, 1, 30, "Input"], Cell[102084, 3260, 85, 1, 30, "Input"], Cell[102172, 3263, 150, 3, 70, "Input"], Cell[102325, 3268, 193, 4, 44, "SmallText"], Cell[CellGroupData[{ Cell[102543, 3276, 258, 4, 90, "Input"], Cell[102804, 3282, 65, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[102918, 3289, 64, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[103007, 3293, 91, 1, 50, "Input"], Cell[103101, 3296, 107, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[103245, 3303, 89, 1, 30, "Input"], Cell[103337, 3306, 206, 5, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[103592, 3317, 36, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[103653, 3321, 38, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[103716, 3325, 297, 6, 130, "Input"], Cell[104016, 3333, 326, 10, 43, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[104391, 3349, 40, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[104456, 3353, 292, 6, 130, "Input"], Cell[104751, 3361, 456, 12, 47, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[105256, 3379, 32, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[105313, 3383, 292, 6, 130, "Input"], Cell[105608, 3391, 476, 12, 47, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[106145, 3410, 33, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[106203, 3414, 44, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[106272, 3418, 289, 6, 130, "Input"], Cell[106564, 3426, 326, 10, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[106939, 3442, 48, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[107012, 3446, 289, 6, 130, "Input"], Cell[107304, 3454, 602, 15, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[107955, 3475, 34, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[108014, 3479, 295, 6, 130, "Input"], Cell[108312, 3487, 656, 15, 70, "Output"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[109029, 3509, 118, 3, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[109172, 3516, 58, 1, 30, "Input"], Cell[109233, 3519, 438, 12, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[109708, 3536, 62, 0, 43, "Subsubsection"], Cell[109773, 3538, 59, 0, 28, "SmallText"], Cell[CellGroupData[{ Cell[109857, 3542, 302, 5, 150, "Input"], Cell[110162, 3549, 369, 10, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[110580, 3565, 64, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[110669, 3569, 302, 5, 150, "Input"], Cell[110974, 3576, 331, 10, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[111354, 3592, 52, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[111431, 3596, 453, 8, 189, "Input"], Cell[111887, 3606, 337, 10, 70, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[112273, 3622, 54, 0, 43, "Subsubsection"], Cell[CellGroupData[{ Cell[112352, 3626, 623, 11, 191, "Input"], Cell[112978, 3639, 330, 10, 70, "Output"] }, Open ]] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[113381, 3657, 131, 6, 39, "Section", Evaluatable->False], Cell[113515, 3665, 118, 3, 33, "Text"], Cell[113636, 3670, 219, 5, 46, "Input"], Cell[113858, 3677, 225, 4, 71, "Text"], Cell[CellGroupData[{ Cell[114108, 3685, 132, 3, 50, "Input"], Cell[114243, 3690, 36, 1, 29, "Output"] }, Open ]], Cell[114294, 3694, 123, 3, 33, "Text"], Cell[114420, 3699, 102, 3, 46, "Input"], Cell[CellGroupData[{ Cell[114547, 3706, 142, 3, 70, "Input"], Cell[114692, 3711, 36, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[114765, 3717, 69, 1, 30, "Input"], Cell[114837, 3720, 175, 3, 29, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[115061, 3729, 107, 3, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[115193, 3736, 33, 0, 47, "Subsection"], Cell[115229, 3738, 215, 4, 50, "Input"], Cell[115447, 3744, 214, 4, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[115698, 3753, 66, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[115789, 3758, 67, 1, 30, "Input"], Cell[115859, 3761, 131, 3, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[116027, 3769, 68, 1, 30, "Input"], Cell[116098, 3772, 201, 4, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[116336, 3781, 81, 1, 30, "Input"], Cell[116420, 3784, 238, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[116695, 3794, 84, 1, 30, "Input"], Cell[116782, 3797, 249, 5, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[117068, 3807, 73, 1, 30, "Input"], Cell[117144, 3810, 55, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[117236, 3816, 76, 1, 30, "Input"], Cell[117315, 3819, 64, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[117416, 3825, 73, 1, 30, "Input"], Cell[117492, 3828, 76, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[117605, 3834, 76, 1, 30, "Input"], Cell[117684, 3837, 85, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[117818, 3844, 75, 1, 31, "Subsection", Evaluatable->False], Cell[117896, 3847, 384, 16, 28, "SmallText"], Cell[118283, 3865, 261, 12, 28, "SmallText"], Cell[118547, 3879, 1652, 33, 152, "Input"], Cell[120202, 3914, 1634, 32, 152, "Input"], Cell[121839, 3948, 393, 16, 50, "Text"], Cell[122235, 3966, 64, 1, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[122336, 3972, 92, 1, 31, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[122453, 3977, 132, 3, 19, "Input", CellOpen->False], Cell[122588, 3982, 12014, 423, 77, 5060, 334, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[134651, 4411, 94, 3, 47, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[134770, 4418, 155, 4, 19, "Input", CellOpen->False], Cell[134928, 4424, 12730, 459, 81, 5591, 368, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[147719, 4890, 165, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[147909, 4900, 56, 0, 47, "Subsection"], Cell[147968, 4902, 136, 3, 28, "SmallText"], Cell[148107, 4907, 222, 5, 30, "Input"], Cell[148332, 4914, 446, 7, 84, "Input"], Cell[148781, 4923, 38, 0, 28, "SmallText"], Cell[148822, 4925, 328, 7, 50, "Input"], Cell[149153, 4934, 42, 0, 28, "SmallText"], Cell[149198, 4936, 229, 5, 63, "Input"], Cell[CellGroupData[{ Cell[149452, 4945, 86, 1, 30, "Input"], Cell[149541, 4948, 308, 8, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[149886, 4961, 88, 1, 30, "Input"], Cell[149977, 4964, 308, 8, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[150334, 4978, 42, 0, 31, "Subsection"], Cell[150379, 4980, 232, 4, 28, "SmallText"], Cell[CellGroupData[{ Cell[150636, 4988, 263, 5, 90, "Input"], Cell[150902, 4995, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[150983, 5001, 263, 5, 90, "Input"], Cell[151249, 5008, 49, 1, 70, "Output"] }, Open ]], Cell[151313, 5012, 86, 1, 30, "Input"], Cell[151402, 5015, 128, 2, 76, "Input"], Cell[151533, 5019, 112, 2, 30, "Input"], Cell[151648, 5023, 129, 3, 30, "Input"], Cell[151780, 5028, 67, 1, 42, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[151884, 5034, 132, 5, 31, "Subsection"], Cell[152019, 5041, 181, 5, 44, "SmallText"], Cell[CellGroupData[{ Cell[152225, 5050, 80, 1, 32, "Input"], Cell[152308, 5053, 40, 1, 70, "Output"] }, Open ]], Cell[152363, 5057, 182, 6, 41, "Input"], Cell[CellGroupData[{ Cell[152570, 5067, 62, 1, 30, "Input"], Cell[152635, 5070, 71, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[152755, 5077, 28, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[152808, 5081, 221, 3, 70, "Input"], Cell[153032, 5086, 10381, 288, 131, 2516, 186, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[163450, 5379, 219, 3, 70, "Input"], Cell[163672, 5384, 9138, 291, 131, 2820, 208, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[172871, 5682, 159, 6, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[173055, 5692, 34, 0, 47, "Subsection"], Cell[173092, 5694, 136, 3, 28, "SmallText"], Cell[173231, 5699, 191, 4, 30, "Input"], Cell[173425, 5705, 36, 0, 28, "SmallText"], Cell[173464, 5707, 349, 8, 50, "Input"], Cell[173816, 5717, 46, 0, 28, "SmallText"], Cell[173865, 5719, 925, 20, 210, "Input"], Cell[174793, 5741, 122, 3, 30, "Input"], Cell[174918, 5746, 109, 2, 50, "Input"], Cell[175030, 5750, 109, 2, 50, "Input"], Cell[175142, 5754, 270, 5, 70, "Input"], Cell[175415, 5761, 191, 4, 30, "Input"], Cell[175609, 5767, 349, 8, 50, "Input"], Cell[175961, 5777, 925, 20, 210, "Input"], Cell[176889, 5799, 122, 3, 30, "Input"], Cell[177014, 5804, 109, 2, 50, "Input"], Cell[177126, 5808, 109, 2, 50, "Input"], Cell[177238, 5812, 270, 5, 70, "Input"], Cell[177511, 5819, 191, 4, 30, "Input"], Cell[177705, 5825, 349, 8, 50, "Input"], Cell[178057, 5835, 122, 3, 30, "Input"], Cell[178182, 5840, 109, 2, 50, "Input"], Cell[178294, 5844, 263, 5, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[178594, 5854, 128, 5, 31, "Subsection"], Cell[178725, 5861, 48, 1, 30, "Input"], Cell[178776, 5864, 48, 1, 30, "Input"], Cell[178827, 5867, 48, 1, 30, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[178912, 5873, 51, 0, 31, "Subsection"], Cell[CellGroupData[{ Cell[178988, 5877, 167, 2, 70, "Input"], Cell[179158, 5881, 4567, 165, 131, 1951, 128, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[183774, 6052, 42, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[183841, 6056, 167, 2, 50, "Input"], Cell[184011, 6060, 9266, 296, 131, 3337, 218, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[193326, 6362, 43, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[193394, 6366, 167, 2, 50, "Input"], Cell[193564, 6370, 5488, 186, 131, 2143, 140, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[199113, 6563, 104, 1, 59, "Section"], Cell[CellGroupData[{ Cell[199242, 6568, 44, 1, 30, "Input"], Cell[199289, 6571, 92, 1, 70, "Output"] }, Open ]], Cell[199396, 6575, 137, 3, 70, "Input"], Cell[199536, 6580, 231, 4, 70, "Input"], Cell[199770, 6586, 237, 4, 70, "Input"], Cell[200010, 6592, 114, 2, 44, "SmallText"], Cell[CellGroupData[{ Cell[200149, 6598, 328, 5, 72, "Input"], Cell[200480, 6605, 43, 1, 70, "Output"] }, Open ]], Cell[200538, 6609, 255, 4, 90, "Input"], Cell[200796, 6615, 257, 4, 90, "Input"], Cell[201056, 6621, 281, 5, 90, "Input"], Cell[201340, 6628, 254, 4, 90, "Input"], Cell[201597, 6634, 254, 4, 90, "Input"], Cell[201854, 6640, 254, 4, 90, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[202145, 6649, 301, 10, 39, "Section"], Cell[CellGroupData[{ Cell[202471, 6663, 42, 0, 47, "Subsection"], Cell[CellGroupData[{ Cell[202538, 6667, 44, 1, 30, "Input"], Cell[202585, 6670, 92, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[202714, 6676, 69, 1, 30, "Input"], Cell[202786, 6679, 70, 1, 70, "Output"] }, Open ]], Cell[202871, 6683, 137, 3, 28, "SmallText"], Cell[203011, 6688, 515, 10, 110, "Input"], Cell[CellGroupData[{ Cell[203551, 6702, 58, 1, 30, "Input"], Cell[203612, 6705, 438, 12, 70, "Output"] }, Open ]], Cell[204065, 6720, 226, 5, 44, "SmallText"], Cell[204294, 6727, 144, 3, 50, "Input"], Cell[204441, 6732, 191, 4, 28, "SmallText"], Cell[204635, 6738, 191, 5, 70, "Input"], Cell[204829, 6745, 347, 6, 70, "Input"], Cell[205179, 6753, 219, 4, 50, "Input"], Cell[205401, 6759, 548, 10, 110, "Input"], Cell[205952, 6771, 197, 3, 50, "Input"], Cell[206152, 6776, 381, 7, 70, "Input"], Cell[206536, 6785, 281, 4, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[206854, 6794, 259, 9, 31, "Subsection"], Cell[207116, 6805, 122, 3, 28, "SmallText"], Cell[207241, 6810, 193, 4, 31, "Input"], Cell[207437, 6816, 193, 4, 31, "Input"], Cell[207633, 6822, 193, 4, 31, "Input"], Cell[CellGroupData[{ Cell[207851, 6830, 801, 15, 130, "Input"], Cell[208655, 6847, 46, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[208750, 6854, 275, 9, 31, "Subsection"], Cell[209028, 6865, 175, 4, 30, "Input"], Cell[209206, 6871, 175, 4, 30, "Input"], Cell[209384, 6877, 175, 4, 30, "Input"], Cell[209562, 6883, 89, 1, 30, "Input"], Cell[209654, 6886, 89, 1, 30, "Input"], Cell[209746, 6889, 89, 1, 30, "Input"], Cell[CellGroupData[{ Cell[209860, 6894, 759, 14, 130, "Input"], Cell[210622, 6910, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[210719, 6917, 260, 9, 31, "Subsection"], Cell[210982, 6928, 122, 3, 28, "SmallText"], Cell[211107, 6933, 214, 4, 31, "Input"], Cell[211324, 6939, 212, 4, 31, "Input"], Cell[CellGroupData[{ Cell[211561, 6947, 446, 7, 110, "Input"], Cell[212010, 6956, 48, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[212095, 6962, 450, 7, 110, "Input"], Cell[212548, 6971, 47, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[212644, 6978, 268, 9, 31, "Subsection"], Cell[212915, 6989, 122, 3, 28, "SmallText"], Cell[213040, 6994, 224, 4, 31, "Input"], Cell[213267, 7000, 229, 4, 31, "Input"], Cell[CellGroupData[{ Cell[213521, 7008, 449, 7, 110, "Input"], Cell[213973, 7017, 49, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[214059, 7023, 446, 7, 110, "Input"], Cell[214508, 7032, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[214605, 7039, 262, 9, 31, "Subsection"], Cell[214870, 7050, 203, 4, 30, "Input"], Cell[215076, 7056, 216, 4, 30, "Input"], Cell[215295, 7062, 230, 4, 30, "Input"], Cell[215528, 7068, 201, 4, 30, "Input"], Cell[215732, 7074, 214, 4, 30, "Input"], Cell[CellGroupData[{ Cell[215971, 7082, 469, 7, 110, "Input"], Cell[216443, 7091, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[216524, 7097, 465, 7, 90, "Input"], Cell[216992, 7106, 44, 1, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[217073, 7112, 471, 7, 110, "Input"], Cell[217547, 7121, 45, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[217641, 7128, 272, 9, 31, "Subsection"], Cell[217916, 7139, 203, 4, 30, "Input"], Cell[218122, 7145, 203, 4, 30, "Input"], Cell[218328, 7151, 203, 4, 30, "Input"], Cell[CellGroupData[{ Cell[218556, 7159, 751, 14, 130, "Input"], Cell[219310, 7175, 46, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[219405, 7182, 293, 9, 31, "Subsection"], Cell[219701, 7193, 108, 3, 28, "SmallText"], Cell[219812, 7198, 206, 3, 50, "Input"], Cell[220021, 7203, 194, 4, 30, "Input"], Cell[220218, 7209, 204, 4, 30, "Input"], Cell[220425, 7215, 92, 1, 30, "Input"], Cell[220520, 7218, 92, 1, 30, "Input"], Cell[220615, 7221, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[220749, 7227, 780, 14, 130, "Input"], Cell[221532, 7243, 48, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[221629, 7250, 274, 9, 31, "Subsection"], Cell[221906, 7261, 102, 2, 28, "SmallText"], Cell[222011, 7265, 202, 3, 50, "Input"], Cell[222216, 7270, 190, 4, 30, "Input"], Cell[222409, 7276, 202, 4, 30, "Input"], Cell[222614, 7282, 92, 1, 30, "Input"], Cell[222709, 7285, 92, 1, 30, "Input"], Cell[222804, 7288, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[222938, 7294, 776, 14, 130, "Input"], Cell[223717, 7310, 47, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[223813, 7317, 266, 9, 31, "Subsection"], Cell[224082, 7328, 203, 4, 30, "Input"], Cell[224288, 7334, 203, 4, 30, "Input"], Cell[224494, 7340, 227, 4, 30, "Input"], Cell[224724, 7346, 92, 1, 30, "Input"], Cell[224819, 7349, 92, 1, 30, "Input"], Cell[224914, 7352, 109, 2, 30, "Input"], Cell[CellGroupData[{ Cell[225048, 7358, 795, 15, 150, "Input"], Cell[225846, 7375, 45, 1, 70, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[225940, 7382, 280, 9, 31, "Subsection"], Cell[226223, 7393, 51, 1, 30, "Input"], Cell[226277, 7396, 275, 5, 91, "Input"], Cell[226555, 7403, 280, 5, 91, "Input"], Cell[226838, 7410, 207, 4, 90, "Input"], Cell[227048, 7416, 212, 4, 90, "Input"], Cell[227263, 7422, 91, 1, 30, "Input"], Cell[227357, 7425, 84, 1, 30, "Input"], Cell[227444, 7428, 1424, 28, 330, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[228917, 7462, 65, 1, 39, "Section", Evaluatable->False], Cell[CellGroupData[{ Cell[229007, 7467, 346, 8, 19, "Input", CellOpen->False], Cell[229356, 7477, 10002, 160, 70, "Output"] }, Open ]] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)