1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Simple Symplectic System</title> 5<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint"> 8<link rel="up" href="../concepts.html" title="Concepts"> 9<link rel="prev" href="symplectic_system.html" title="Symplectic System"> 10<link rel="next" href="implicit_system.html" title="Implicit System"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td> 15<td align="center"><a href="../../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="implicit_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="boost_numeric_odeint.concepts.simple_symplectic_system"></a><a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple 28 Symplectic System</a> 29</h3></div></div></div> 30<h5> 31<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h0"></a> 32 <span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.description"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.description">Description</a> 33 </h5> 34<p> 35 In most Hamiltonian systems the kinetic term is a quadratic term in the momentum 36 <span class="emphasis"><em>H<sub>kin</sub> = p^2 / 2m</em></span> and in many cases it is possible to rescale 37 coordinates and set <span class="emphasis"><em>m=1</em></span> which leads to a trivial equation 38 of motion: 39 </p> 40<p> 41 <span class="emphasis"><em>q'(t) = f(p) = p. </em></span> 42 </p> 43<p> 44 while for <span class="emphasis"><em>p'</em></span> we still have the general form 45 </p> 46<p> 47 <span class="emphasis"><em>p'(t) = g(q) </em></span> 48 </p> 49<p> 50 As this case is very frequent we introduced a concept where only the nontrivial 51 equation for <span class="emphasis"><em>p'</em></span> has to be provided to the symplectic 52 stepper. We call this concept <span class="emphasis"><em>SimpleSymplecticSystem</em></span> 53 </p> 54<h5> 55<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h1"></a> 56 <span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.notation"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.notation">Notation</a> 57 </h5> 58<div class="variablelist"> 59<p class="title"><b></b></p> 60<dl class="variablelist"> 61<dt><span class="term">System</span></dt> 62<dd><p> 63 A type that is a model of SimpleSymplecticSystem 64 </p></dd> 65<dt><span class="term">Coor</span></dt> 66<dd><p> 67 The type of the coordinate <span class="emphasis"><em>q</em></span> 68 </p></dd> 69<dt><span class="term">MomentumDeriv</span></dt> 70<dd><p> 71 The type of the derivative of momentum <span class="emphasis"><em>p'</em></span> 72 </p></dd> 73<dt><span class="term">sys</span></dt> 74<dd><p> 75 An object that models System 76 </p></dd> 77<dt><span class="term">q</span></dt> 78<dd><p> 79 Object of type Coor 80 </p></dd> 81<dt><span class="term">dpdt</span></dt> 82<dd><p> 83 Object of type MomentumDeriv 84 </p></dd> 85</dl> 86</div> 87<h5> 88<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h2"></a> 89 <span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.valid_expressions"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.valid_expressions">Valid 90 Expressions</a> 91 </h5> 92<div class="informaltable"><table class="table"> 93<colgroup> 94<col> 95<col> 96<col> 97<col> 98</colgroup> 99<thead><tr> 100<th> 101 <p> 102 Name 103 </p> 104 </th> 105<th> 106 <p> 107 Expression 108 </p> 109 </th> 110<th> 111 <p> 112 Type 113 </p> 114 </th> 115<th> 116 <p> 117 Semantics 118 </p> 119 </th> 120</tr></thead> 121<tbody> 122<tr> 123<td> 124 <p> 125 Check for pair 126 </p> 127 </td> 128<td> 129 <p> 130 <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_pair</span><span class="special"><</span> 131 <span class="identifier">System</span> <span class="special">>::</span><span class="identifier">type</span></code> 132 </p> 133 </td> 134<td> 135 <p> 136 <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code> 137 </p> 138 </td> 139<td> 140 <p> 141 Check if System is a pair, should be evaluated to false in this 142 case. 143 </p> 144 </td> 145</tr> 146<tr> 147<td> 148 <p> 149 Calculate <span class="emphasis"><em>dp/dt = g(q)</em></span> 150 </p> 151 </td> 152<td> 153 <p> 154 <code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span> 155 <span class="identifier">q</span> <span class="special">,</span> 156 <span class="identifier">dpdt</span> <span class="special">)</span></code> 157 </p> 158 </td> 159<td> 160 <p> 161 <code class="computeroutput"><span class="keyword">void</span></code> 162 </p> 163 </td> 164<td> 165 <p> 166 Calculates <span class="emphasis"><em>g(q)</em></span>, the result is stored into 167 <code class="computeroutput"><span class="identifier">dpdt</span></code> 168 </p> 169 </td> 170</tr> 171</tbody> 172</table></div> 173</div> 174<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 175<td align="left"></td> 176<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 177 Distributed under the Boost Software License, Version 1.0. (See accompanying 178 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 179 </p> 180</div></td> 181</tr></table> 182<hr> 183<div class="spirit-nav"> 184<a accesskey="p" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="implicit_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 185</div> 186</body> 187</html> 188
