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| <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> |
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