(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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[ 6715, 234]*) (*NotebookOutlinePosition[ 7450, 260]*) (* CellTagsIndexPosition[ 7406, 256]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Cin\[EAcute]matique vectorielle. Corrig\[EAcute] de \ l'exercice 4.", "Title", FontSize->18]], "Subsubsection"], Cell["D\[EAcute]finissons l'horaire du mobile :", "Text", FormatType->TextForm], Cell[BoxData[ \(r[t_] := {x0, y0} + {vx0, vy0} t + {ax0, ay0} t^2\)], "Input"], Cell["\<\ Calculons les coordonn\[EAcute]es du vecteur position pour les donn\ \[EAcute]es du probl\[EGrave]me :\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(x0 = 0;\)\), "\[IndentingNewLine]", \(\(y0 = 0;\)\), "\[IndentingNewLine]", \(\(vx0 = 4;\)\), "\[IndentingNewLine]", \(\(vy0 = 0;\)\), "\[IndentingNewLine]", \(\(ax0 = \(-2\);\)\), "\[IndentingNewLine]", \(\(ay0 = 1;\)\), "\[IndentingNewLine]", \(\(tmin = \(-3\);\)\), "\[IndentingNewLine]", \(tmax = \ 3; \ (*\ temps\ de\ simulation\ *) \[IndentingNewLine]\[CapitalDelta]t = 1; \ \ (*\ intervalle\ de\ temps\ entre\ deux\ positions\ successives\ \ *) \[IndentingNewLine]c = 1.05; \ (*\ coefficient\ permettant\ de\ modifier\ le\ PlotRange\ \ *) \[IndentingNewLine]ps = 5; \ \ (*\ AbsolutePointSize\ *) \[IndentingNewLine]fs = 12; \ (*\ FontSize\ *) \[IndentingNewLine]coord = Table[r[t], {t, tmin, tmax, \[CapitalDelta]t}]\)}], "Input"], Cell[BoxData[ \({{\(-30\), 9}, {\(-16\), 4}, {\(-6\), 1}, {0, 0}, {2, 1}, {0, 4}, {\(-6\), 9}}\)], "Output"] }, Open ]], Cell[TextData[{ "Calculons les composantes ", Cell[BoxData[ FormBox[ StyleBox[\(v\_x\), FontSlant->"Italic"], TextForm]]], " = ", StyleBox["\[CapitalDelta]x", FontSlant->"Italic"], "/", StyleBox["\[CapitalDelta]t", FontSlant->"Italic"], " du vecteur vitesse :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(-Apply[Subtract, Partition[\(Transpose[coord]\)[\([1]\)], 2, 1], 1]\)\)], "Input"], Cell[BoxData[ \({14, 10, 6, 2, \(-2\), \(-6\)}\)], "Output"] }, Open ]], Cell[TextData[{ "Calculons les composantes ", Cell[BoxData[ FormBox[ StyleBox[\(v\_y\), FontSlant->"Italic"], TextForm]]], " = ", StyleBox["\[CapitalDelta]y", FontSlant->"Italic"], "/", StyleBox["\[CapitalDelta]t", FontSlant->"Italic"], " du vecteur vitesse :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(-Apply[Subtract, Partition[\(Transpose[coord]\)[\([2]\)], 2, 1], 1]\)\)], "Input"], Cell[BoxData[ \({\(-5\), \(-3\), \(-1\), 1, 3, 5}\)], "Output"] }, Open ]], Cell[TextData[{ "Regroupons ces composantes sous la forme {", Cell[BoxData[ FormBox[ StyleBox[\(v\_x\), FontSlant->"Italic"], TextForm]]], ", ", Cell[BoxData[ FormBox[ StyleBox[\(v\_y\), FontSlant->"Italic"], TextForm]]], "} :" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Transpose[{\(-Apply[Subtract, Partition[\(Transpose[coord]\)[\([1]\)], 2, 1], 1]\), \(-Apply[ Subtract, Partition[\(Transpose[coord]\)[\([2]\)], 2, 1], 1]\)}]\)], "Input"], Cell[BoxData[ \({{14, \(-5\)}, {10, \(-3\)}, {6, \(-1\)}, {2, 1}, {\(-2\), 3}, {\(-6\), 5}}\)], "Output"] }, Open ]], Cell["\<\ Calculons la grandeur du vecteur vitesse de seconde en seconde \ :\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(v = Map[Sqrt[# . #] &, %]\)], "Input"], Cell[BoxData[ \({\@221, \@109, \@37, \@5, \@13, \@61}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["N. 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