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diff --git a/libs/numeric/odeint/doc/html/boost_numeric_odeint/concepts/second_order_system.html b/libs/numeric/odeint/doc/html/boost_numeric_odeint/concepts/second_order_system.html new file mode 100644 index 0000000000..72e8a176c6 --- /dev/null +++ b/libs/numeric/odeint/doc/html/boost_numeric_odeint/concepts/second_order_system.html @@ -0,0 +1,169 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Second Order System</title> +<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> +<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint"> +<link rel="up" href="../concepts.html" title="Concepts"> +<link rel="prev" href="system.html" title="System"> +<link rel="next" href="symplectic_system.html" title="Symplectic System"> +</head> +<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> +<table cellpadding="2" width="100%"><tr> +<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td> +<td align="center"><a href="../../../../../../../index.html">Home</a></td> +<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td> +<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> +<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> +<td align="center"><a href="../../../../../../../more/index.htm">More</a></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<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> +</div> +<div class="section"> +<div class="titlepage"><div><div><h3 class="title"> +<a name="boost_numeric_odeint.concepts.second_order_system"></a><a class="link" href="second_order_system.html" title="Second Order System">Second + Order System</a> +</h3></div></div></div> +<h5> +<a name="boost_numeric_odeint.concepts.second_order_system.h0"></a> + <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> + </h5> +<p> + The Second Order System concept models the algorithmic implementation of + the rhs for steppers requirering the second order derivative, hence the r.h.s. + of the ODE <span class="emphasis"><em>x'' = f(x,x',t)</em></span>. The only requirement for + this concept is that it should be callable with a specific parameter syntax + (see below). A Second Order System is typically implemented as a function + or a functor. Systems fulfilling this concept are required by the Velocity + Verlet method. + </p> +<h5> +<a name="boost_numeric_odeint.concepts.second_order_system.h1"></a> + <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> + </h5> +<div class="variablelist"> +<p class="title"><b></b></p> +<dl class="variablelist"> +<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt> +<dd><p> + A type that is a model of Second Order System + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">Space</span></code></span></dt> +<dd><p> + A type representing the state <span class="emphasis"><em>x</em></span> of the ODE + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">Velocity</span></code></span></dt> +<dd><p> + A type representing the derivative <span class="emphasis"><em>x'</em></span> of the ODE + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">Acceleration</span></code></span></dt> +<dd><p> + A type representing the second order derivative <span class="emphasis"><em>x''</em></span> + of the ODE + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt> +<dd><p> + A type representing the time + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt> +<dd><p> + An object of type <code class="computeroutput"><span class="identifier">System</span></code> + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt> +<dd><p> + Object of type <code class="computeroutput"><span class="identifier">Space</span></code> + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">v</span></code></span></dt> +<dd><p> + Object of type <code class="computeroutput"><span class="identifier">Velocity</span></code> + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">a</span></code></span></dt> +<dd><p> + Object of type <code class="computeroutput"><span class="identifier">Acceleration</span></code> + </p></dd> +<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt> +<dd><p> + Object of type <code class="computeroutput"><span class="identifier">Time</span></code> + </p></dd> +</dl> +</div> +<h5> +<a name="boost_numeric_odeint.concepts.second_order_system.h2"></a> + <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 + expressions</a> + </h5> +<div class="informaltable"><table class="table"> +<colgroup> +<col> +<col> +<col> +<col> +</colgroup> +<thead><tr> +<th> + <p> + Name + </p> + </th> +<th> + <p> + Expression + </p> + </th> +<th> + <p> + Type + </p> + </th> +<th> + <p> + Semantics + </p> + </th> +</tr></thead> +<tbody><tr> +<td> + <p> + Calculate <span class="emphasis"><em>x'' := f(x,x',t)</em></span> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span> + <span class="identifier">x</span> <span class="special">,</span> + <span class="identifier">v</span> <span class="special">,</span> + <span class="identifier">a</span> <span class="special">,</span> + <span class="identifier">t</span> <span class="special">)</span></code> + </p> + </td> +<td> + <p> + <code class="computeroutput"><span class="keyword">void</span></code> + </p> + </td> +<td> + <p> + Calculates f(x,x',t), the result is stored into a. + </p> + </td> +</tr></tbody> +</table></div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2009-2012 Karsten + Ahnert and Mario Mulansky<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + 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>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<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> +</div> +</body> +</html> |