1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Second Order 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="system.html" title="System"> 10<link rel="next" href="symplectic_system.html" title="Symplectic 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="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="symplectic_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.second_order_system"></a><a class="link" href="second_order_system.html" title="Second Order System">Second 28 Order System</a> 29</h3></div></div></div> 30<h5> 31<a name="boost_numeric_odeint.concepts.second_order_system.h0"></a> 32 <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.description"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.description">Description</a> 33 </h5> 34<p> 35 The Second Order System concept models the algorithmic implementation of 36 the rhs for steppers requirering the second order derivative, hence the r.h.s. 37 of the ODE <span class="emphasis"><em>x'' = f(x,x',t)</em></span>. The only requirement for 38 this concept is that it should be callable with a specific parameter syntax 39 (see below). A Second Order System is typically implemented as a function 40 or a functor. Systems fulfilling this concept are required by the Velocity 41 Verlet method. 42 </p> 43<h5> 44<a name="boost_numeric_odeint.concepts.second_order_system.h1"></a> 45 <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.notation"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.notation">Notation</a> 46 </h5> 47<div class="variablelist"> 48<p class="title"><b></b></p> 49<dl class="variablelist"> 50<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt> 51<dd><p> 52 A type that is a model of Second Order System 53 </p></dd> 54<dt><span class="term"><code class="computeroutput"><span class="identifier">Space</span></code></span></dt> 55<dd><p> 56 A type representing the state <span class="emphasis"><em>x</em></span> of the ODE 57 </p></dd> 58<dt><span class="term"><code class="computeroutput"><span class="identifier">Velocity</span></code></span></dt> 59<dd><p> 60 A type representing the derivative <span class="emphasis"><em>x'</em></span> of the ODE 61 </p></dd> 62<dt><span class="term"><code class="computeroutput"><span class="identifier">Acceleration</span></code></span></dt> 63<dd><p> 64 A type representing the second order derivative <span class="emphasis"><em>x''</em></span> 65 of the ODE 66 </p></dd> 67<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt> 68<dd><p> 69 A type representing the time 70 </p></dd> 71<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt> 72<dd><p> 73 An object of type <code class="computeroutput"><span class="identifier">System</span></code> 74 </p></dd> 75<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt> 76<dd><p> 77 Object of type <code class="computeroutput"><span class="identifier">Space</span></code> 78 </p></dd> 79<dt><span class="term"><code class="computeroutput"><span class="identifier">v</span></code></span></dt> 80<dd><p> 81 Object of type <code class="computeroutput"><span class="identifier">Velocity</span></code> 82 </p></dd> 83<dt><span class="term"><code class="computeroutput"><span class="identifier">a</span></code></span></dt> 84<dd><p> 85 Object of type <code class="computeroutput"><span class="identifier">Acceleration</span></code> 86 </p></dd> 87<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt> 88<dd><p> 89 Object of type <code class="computeroutput"><span class="identifier">Time</span></code> 90 </p></dd> 91</dl> 92</div> 93<h5> 94<a name="boost_numeric_odeint.concepts.second_order_system.h2"></a> 95 <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.valid_expressions"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.valid_expressions">Valid 96 expressions</a> 97 </h5> 98<div class="informaltable"><table class="table"> 99<colgroup> 100<col> 101<col> 102<col> 103<col> 104</colgroup> 105<thead><tr> 106<th> 107 <p> 108 Name 109 </p> 110 </th> 111<th> 112 <p> 113 Expression 114 </p> 115 </th> 116<th> 117 <p> 118 Type 119 </p> 120 </th> 121<th> 122 <p> 123 Semantics 124 </p> 125 </th> 126</tr></thead> 127<tbody><tr> 128<td> 129 <p> 130 Calculate <span class="emphasis"><em>x'' := f(x,x',t)</em></span> 131 </p> 132 </td> 133<td> 134 <p> 135 <code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span> 136 <span class="identifier">x</span> <span class="special">,</span> 137 <span class="identifier">v</span> <span class="special">,</span> 138 <span class="identifier">a</span> <span class="special">,</span> 139 <span class="identifier">t</span> <span class="special">)</span></code> 140 </p> 141 </td> 142<td> 143 <p> 144 <code class="computeroutput"><span class="keyword">void</span></code> 145 </p> 146 </td> 147<td> 148 <p> 149 Calculates f(x,x',t), the result is stored into a. 150 </p> 151 </td> 152</tr></tbody> 153</table></div> 154</div> 155<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 156<td align="left"></td> 157<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p> 158 Distributed under the Boost Software License, Version 1.0. (See accompanying 159 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>) 160 </p> 161</div></td> 162</tr></table> 163<hr> 164<div class="spirit-nav"> 165<a accesskey="p" href="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="symplectic_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a> 166</div> 167</body> 168</html> 169
