Talk:PlanetPhysics/Maple for Planet Physics

Original TeX Content from PlanetPhysics Archive
%%% This file is part of PlanetPhysics snapshot of 2011-09-01 %%% Primary Title: Maple for PlanetPhysics %%% Primary Category Code: 01.30.Xx %%% Filename: MapleForPlanetPhysics.tex %%% Version: 9 %%% Owner: bloftin %%% Author(s): bloftin %%% PlanetPhysics is released under the GNU Free Documentation License. %%% You should have received a file called fdl.txt along with this file. %%% If not, please write to gnu@gnu.org. \documentclass[12pt]{article} \usepackage{syntonly} \pagestyle{empty} \setlength{\paperwidth}{8.5in} \setlength{\paperheight}{11in}

\setlength{\topmargin}{0.00in} \setlength{\headsep}{0.00in} \setlength{\headheight}{0.00in} \setlength{\evensidemargin}{0.00in} \setlength{\oddsidemargin}{0.00in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.00in} \setlength{\voffset}{0.00in} \setlength{\hoffset}{0.00in} \setlength{\marginparwidth}{0.00in} \setlength{\marginparsep}{0.00in} \setlength{\parindent}{0.00in} \setlength{\parskip}{0.15in}

\usepackage{html}

% this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners.

% almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts}

% used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) \usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic}

% there are many more packages, add them here as you need them \usepackage{maplestd2e} % define commands here

\syntaxonly \begin{document}

\begin{maplelatex}\mapleinline{inert}{2d}{%[poincare, generate_ic, zoom, hamilton_eqs]}{ $[{\it poincare},{\it generate\_ic},{\it zoom},{\it hamilton\_eqs}\\ \mbox{}]$} \end{maplelatex}\begin{maplelatex}\begin{Maple Heading 1}{\textbf{The Toda \htmladdnormallink{Hamiltonian}{http://planetphysics.us/encyclopedia/Hamiltonian2.html}}}\end{Maple Heading 1} \end{maplelatex} \begin{maplelatex}\begin{Maple Normal}{\textbf{Reference:}A.J. Lichtenberg and M.A. Lieberman, "\htmladdnormallink{regular}{http://planetphysics.us/encyclopedia/CoIntersections.html} and Stochastic \htmladdnormallink{motion",}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} \textit{Applied Mathematical Sciences} 38 (New York: Springer Verlag, 1994).}\end{Maple Normal} \textbf{H := 1/2*(p1\symbol{94}2 + p2\symbol{94}2) + 1/24*(exp(2*q2+2*sqrt(3)*q1) + exp(2*q2-2*sqrt(3)*q1) + exp(-4*q2))-1/8;}\end{maplelatex} \mapleresult \begin{maplelatex}\mapleinline{inert}{2d}{%H := p1^2/2+p2^2/2+1/24*exp(2*q2+2*3^(1/2)*q1)+1/24*exp(2*q2-2*3^(1/2)*q1)+1/24*exp(-4*q2)-1/8}{ $H\, := \,1/2\,^{2}+1/2\,^{2}+1/24\,{e^{2\,{\it q2}+2\,\sqrt {3}{\it q1}}}\\ \mbox{}+1/24\,{e^{2\,{\it q2}-2\,\sqrt {3}{\it q1}}}+1/24\,{e^{-4\,{\it q2}}}-1/8$} \end{maplelatex}\begin{mapleinput} \mapleinline{active}{1d}{\textbf{H, t=-150..150, \{[0,.1,1.4,.1,0]\}:}}{} \end{mapleinput} \begin{mapleinput} \mapleinline{active}{1d}{\begin{Maple Normal}{\textbf{poincare(%, stepsize=.05,iterations=5);}(12 sec.)}\end{Maple Normal} }{} \end{mapleinput}

\mapleresult \begin{maplelatex}\mapleinline{inert}{2d}{%_____________________________________________________}{ \[{\it \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\]} \end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`H = .99005020`, ` Initial conditions:`, t = 0, p1 = .1, p2 = 1.4, q1 = .1, q2 = 0}{ $\mbox ,\,\mbox ,\,t=0,\,{\it p1}= 0.1,\,{\it p2}= 1.4,\,{\it q1}= 0.1,\,{\it q2}=0$} \end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Number of points found crossing the (p1,q1) plane: 127`}{ $\mbox $} \end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Maximum H deviation : .5740000000e-5 %`}{ $\mbox $} \end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%_____________________________________________________}{ \[{\it \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\]} \end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Time consumed: 12 seconds`}{ $\mbox $} \end{maplelatex}

\medskip \begin{figure} \includegraphics{poly.eps} \end{figure} \medskip

\begin{maplelatex}\begin{Maple Normal}{Figure 1.a. shows a 2-D surface-of-section (2PS) over the q2=0 plane, with 127 intersection points lying on smooth curves. }\end{Maple Normal} \end{maplelatex}\begin{mapleinput} \mapleinline{active}{1d}{\begin{Maple Normal}{\textbf{poincare(%%,stepsize=.05,iterations=5,scene=[p2,q2]);}(13 sec.)}\end{Maple Normal} }{} \end{mapleinput}

\end{document}