(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = leftheader, inactive, L2, 12, "Times"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; fontset = leftfooter, inactive, L2, 12, "Times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; paletteColors = 128; currentKernel; ] :[font = subsubsection; inactive; Cclosed; preserveAspect; startGroup] Legal Notice, Disclaimer, and Book Ordering Information: :[font = input; inactive; preserveAspect; endGroup] (* Legal Notice, Disclaimer, and Book Ordering Information: Last Modified: FIO January 1, 1995 Mathematica For Physics Robert L. Zimmerman and Fredrick I. Olness MathSource Number: 0206-862 ISBN 0-201-53796-6 For ordering information, call 1-800-822-6339 Addison-Wesley Publishing Company Communication with the authors: Fredrick I. Olness: olness@mail.physics.smu.edu Robert L. Zimmerman: bob@zim.uoregon.edu Copyright 1995, Addison-Wesley Publishing Company, Inc. The material in this file may be distributed freely so long as the content remains unchanged, and the copyright and reference notices are included. The publisher grants permission for the noncommercial use of these programs and program segments. All other uses require the prior written consent of the publisher. All rights are reserved with regard to the material in the "Mathematica For Physics" text, and may not be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. The programs and applications presented in this book have been included for their instructional value. They have been tested with care but are not guaranteed for any particular purpose. The publisher does not offer any warranties or representations, nor does it accept any liabilities with respect to the programs or applications. *) :[font = subsection; inactive; preserveAspect] Chapter 3, Section 3, Problem 3: Double Pendulum Code to Generate Animation ONLY!!! :[font = input; preserveAspect] Clear["Global`*"]; :[font = input; preserveAspect] line[c1_,c2_]=Line[{{0, 0}, {Sin[(c1*Cos[(2/3)^(1/2)*t] - c2*Cos[2^(1/2)*t])/5^(1/2)], -Cos[(c1*Cos[(2/3)^(1/2)*t] - c2*Cos[2^(1/2)*t])/5^(1/2)]}, {Sin[(c1*Cos[(2/3)^(1/2)*t] - c2*Cos[2^(1/2)*t])/5^(1/2)] + Sin[(2*(c1*Cos[(2/3)^(1/2)*t] + c2*Cos[2^(1/2)*t]))/5^(1/2)], -Cos[(c1*Cos[(2/3)^(1/2)*t] - c2*Cos[2^(1/2)*t])/5^(1/2)] - Cos[(2*(c1*Cos[(2/3)^(1/2)*t] + c2*Cos[2^(1/2)*t]))/5^(1/2)]}}]; :[font = input; preserveAspect] frames=25; Do[ Show[ Graphics[ line[0,1] //N ,PlotRange->{{-2,2},{0,-2}}] ] ,{t,1,25,25/frames}]; :[font = input; preserveAspect] frames=25; Do[ Show[ Graphics[ line[1,0] //N ,PlotRange->{{-2,2},{0,-2}}] ] ,{t,1,25,25/frames}]; :[font = input; preserveAspect; animationSpeed = 14] frames=25; Do[ Show[ Graphics[ line[0.5,0.5] //N ,PlotRange->{{-2,2},{0,-2}}] ] ,{t,1,25,25/frames}]; ^*)