(************** 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). 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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[ 3625335, 149591]*) (*NotebookOutlinePosition[ 3625973, 149613]*) (* CellTagsIndexPosition[ 3625929, 149609]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Satellite orbit", "Subtitle", CellAutoOverwrite->False], Cell["\<\ Ivan Cnop icnop@vub.ac.be\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Problem", "Section", CellAutoOverwrite->False], Cell["\<\ Plot the orbit of a spy satellite watching over all countries in a \ zone of 45 degrees on either side of the equator. \ \>", "Subsubsection", CellAutoOverwrite->False] }, Closed]], 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A . {x[t], y[t], z[t]} // N\)], "Input", CellAutoOverwrite->False], Cell[BoxData[ \({Cos[0.125`\ t]\ Cos[2.5`\ t] + 0.7071067811865475`\ Sin[0.125`\ t]\ Sin[2.5`\ t], \(-1.`\)\ Cos[ 2.5`\ t]\ Sin[0.125`\ t] + 0.7071067811865475`\ Cos[0.125`\ t]\ Sin[2.5`\ t], 0.7071067811865475`\ Sin[2.5`\ t]}\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(curve[t]\)], "Input", CellAutoOverwrite->False], Cell[BoxData[ \({Cos[0.125`\ t]\ Cos[2.5`\ t] + 0.7071067811865475`\ Sin[0.125`\ t]\ Sin[2.5`\ t], \(-1.`\)\ Cos[ 2.5`\ t]\ Sin[0.125`\ t] + 0.7071067811865475`\ Cos[0.125`\ t]\ Sin[2.5`\ t], 0.7071067811865475`\ Sin[2.5`\ t]}\)], "Output"] }, Closed]], Cell["\<\ The action is given by a rather complicated 3x3 matrix, difficult \ to guess off-hand:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(B[t] . 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