(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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). 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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[ 467579, 15702]*) (*NotebookOutlinePosition[ 512900, 17272]*) (* CellTagsIndexPosition[ 512761, 17264]*) (*WindowFrame->Normal*) Notebook[{ Cell[GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg"], "Graphics", ShowCellBracket->False, CellMargins->{{25, 24}, {5, 7}}, ImageSize->{81, 22}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}], Cell[TextData[{ "2D and 3D Measurements\n", StyleBox[ "Authors: Bill Davis, Horacio Porta and Jerry Uhl ", "Subtitle"], StyleBox["\[Copyright]1999", "Subtitle", FontSize->12], StyleBox["\nProducer: Bruce Carpenter\n", "Subtitle"], StyleBox["Publisher: ", "Subtitle", FontSize->12], StyleBox[ButtonBox["Math Everywhere, Inc.", ButtonData:>{ URL[ "http://www.matheverywhere.com"], None}, ButtonStyle->"MEIHyperlink"], FontSize->12], StyleBox[" Distributor: ", "Subtitle", FontSize->12], StyleBox[ButtonBox["Wolfram Research, Inc.", ButtonData:>{ URL[ "http://www.wolfram.com"], None}, ButtonStyle->"MEIHyperlink", ButtonNote->"Makers of Mathematica!"], FontSize->12] }], "PrefaceTitle", CellMargins->{{Inherited, Inherited}, {Inherited, 0}}], Cell[TextData[{ "VC.01 Vectors Point the Way \n", StyleBox[" Sampler", FontSize->16, FontSlant->"Italic"] }], "Title"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " Initializations" }], "Special2"], Cell[BoxData[{ \(\(Off[General::spell];\)\), "\n", \(\(Off[General::spell1];\)\), "\n", \(\(Off[ParametricPlot3D::ppcom];\)\), "\n", \(\(Off[ParametricPlot::ppcom];\)\), "\n", \(\(Off[Plot::plnr];\)\), "\n", \(\(SetOptions[Limit, Analytic \[Rule] True];\)\)}], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[BoxData[ \(\(CMView = {2.7, 1.6, 1.2};\)\)], "Input", InitializationCell->True, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Vector Drawer", "Subsubsection"], Cell["\<\ (* :Date: Copyright 1999, Math Everywhere, Inc. *) (* :Drawbacks: Since the vectors are drawn out of context, the shapes of the arrowheads are only correct with AspectRatio set to Automatic. *) BeginPackage[\"Vector3D`\",\"Graphics`Colors`\"];\ \>", "Input", InitializationCell->True], Cell[CellGroupData[{ Cell["\<\ Axes3D::usage = \"Axes3D[a, b] creates a Graphics3D object of \ cartesian axes with x, y, and z running from -a/3 to a, and with axes labels \ b units beyond the tips of the axes. 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Cell[BoxData[ \(t\)]], ", an object is at the location \n ", Cell[BoxData[ \(P[t] = {x[t], y[t]}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[t, x, y, P];\)\), "\n", \(P[t_] = {x[t], y[t]}\)}], "Input", AspectRatioFixed->True], Cell[BoxData[ \({x[t], y[t]}\)], "Output"] }, Open ]], Cell[TextData[{ "The velocity of the object at time ", Cell[BoxData[ \(t\)]], " is given by:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[vel];\)\), "\n", \(vel[t_] = D[P[t], \ t]\)}], "Input", AspectRatioFixed->True], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{ SuperscriptBox["x", "\[Prime]", MultilineFunction->None], "[", "t", "]"}], ",", RowBox[{ SuperscriptBox["y", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}], "}"}]], "Output"] }, Open ]], Cell[TextData[{ "The velocity is a vector quantity. 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