(************** 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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L s .73151 .45935 m .71957 .44817 L s .70279 .35241 m .68804 .34361 L s .45178 .59268 m .4405 .60351 L s .44072 .30256 m .42823 .29312 L s .63081 .27519 m .61613 .28223 L s .39382 .35166 m .37934 .36074 L s .51152 .26958 m .49495 .26529 L s .39461 .53915 m .38388 .55045 L s .52483 .26574 m .50741 .26846 L s .54231 .26348 m .52483 .26574 L s .50741 .26846 m .49008 .27165 L s .6015 .26445 m .585 .26874 L s .57181 .26601 m .55432 .26376 L s .58923 .26873 m .57181 .26601 L s .55432 .26376 m .53679 .26198 L s .36505 .45828 m .35339 .46952 L s .55982 .26171 m .54231 .26348 L s .60655 .27192 m .58923 .26873 L s .66769 .29124 m .65535 .30068 L s .49008 .27165 m .47287 .2753 L s .53679 .26198 m .51926 .26069 L s .7172 .36148 m .70279 .35241 L s .73123 .38581 m .72231 .39943 L s .62373 .27557 m .60655 .27192 L s .57732 .26041 m .55982 .26171 L s .47287 .2753 m .45582 .27941 L s .70264 .32234 m .69258 .33404 L s .71269 .55164 m .70206 .54039 L s .51926 .26069 m .50176 .25988 L s .46542 .27656 m 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s .8417 .46908 m .83012 .45564 L s .75779 .23192 m .74187 .23534 L s .3477 .23532 m .33171 .23217 L s .77631 .25021 m .75877 .24857 L s .33045 .24981 m .31291 .25172 L s .29541 .29264 m .27851 .29995 L s .78616 .63462 m .77686 .62341 L s .81108 .29708 m .7941 .29 L s .34112 .23456 m .32832 .22737 L s .82705 .5701 m .81821 .55716 L s .25887 .37306 m .24494 .38479 L s .84568 .38088 m .83164 .36928 L s .24997 .47324 m .23952 .48674 L s .85226 .48256 m .8417 .46908 L s .77313 .22935 m .75779 .23192 L s .33171 .23217 m .3163 .22987 L s .79317 .25269 m .77631 .25021 L s .31291 .25172 m .29605 .25446 L s .27851 .29995 m .26247 .30794 L s .8272 .30486 m .81108 .29708 L s .24494 .38479 m .23204 .39689 L s .85871 .39286 m .84568 .38088 L s .7947 .64519 m .78616 .63462 L s .32832 .22737 m .31613 .221 L s .83494 .58267 m .82705 .5701 L s .23952 .48674 m .23013 .50022 L s .86176 .49603 m .85226 .48256 L s .78783 .22766 m .77313 .22935 L s .80929 .256 m .79317 .25269 L s .29605 .25446 m .27994 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L s .87776 .52351 m .87057 .51022 L s .30475 .21559 m .29392 .21095 L s .80938 .66432 m .80249 .65519 L s .84786 .60692 m .84203 .59524 L s .23437 .32506 m .22119 .33489 L s .79785 .21003 m .78725 .21476 L s .26557 .26215 m .25111 .26732 L s .8711 .33315 m .85803 .32339 L s .21061 .42062 m .20097 .43354 L s .84078 .26582 m .82646 .26074 L s .28803 .22795 m .27474 .2283 L s .81694 .22708 m .80384 .22683 L s .89182 .43174 m .88228 .41884 L s .21554 .52514 m .20942 .53826 L s .88375 .53664 m .87776 .52351 L s .24565 .60826 m .24071 .61938 L s .22119 .33489 m .20913 .3453 L s .29392 .21095 m .28386 .20725 L s .85264 .61807 m .84786 .60692 L s .25111 .26732 m .23761 .27331 L s .81539 .67268 m .80938 .66432 L s .88305 .34351 m .8711 .33315 L s .80768 .20623 m .79785 .21003 L s .20097 .43354 m .19256 .44666 L s .85413 .27173 m .84078 .26582 L s .27474 .2283 m .26228 .22958 L s .90012 .44485 m .89182 .43174 L s .8292 .22826 m .81694 .22708 L s .20942 .53826 m .20452 .55114 L s .20913 .3453 m 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