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- <div class="titlepage"><div><div><h3 class="title">
- <a name="boost_numeric_odeint.concepts.simple_symplectic_system"></a><a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple
- Symplectic System</a>
- </h3></div></div></div>
- <h5>
- <a name="boost_numeric_odeint.concepts.simple_symplectic_system.h0"></a>
- <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>
- </h5>
- <p>
- In most Hamiltonian systems the kinetic term is a quadratic term in the momentum
- <span class="emphasis"><em>H<sub>kin</sub> = p^2 / 2m</em></span> and in many cases it is possible to rescale
- coordinates and set <span class="emphasis"><em>m=1</em></span> which leads to a trivial equation
- of motion:
- </p>
- <p>
- <span class="emphasis"><em>q'(t) = f(p) = p. </em></span>
- </p>
- <p>
- while for <span class="emphasis"><em>p'</em></span> we still have the general form
- </p>
- <p>
- <span class="emphasis"><em>p'(t) = g(q) </em></span>
- </p>
- <p>
- As this case is very frequent we introduced a concept where only the nontrivial
- equation for <span class="emphasis"><em>p'</em></span> has to be provided to the symplectic
- stepper. We call this concept <span class="emphasis"><em>SimpleSymplecticSystem</em></span>
- </p>
- <h5>
- <a name="boost_numeric_odeint.concepts.simple_symplectic_system.h1"></a>
- <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>
- </h5>
- <div class="variablelist">
- <p class="title"><b></b></p>
- <dl class="variablelist">
- <dt><span class="term">System</span></dt>
- <dd><p>
- A type that is a model of SimpleSymplecticSystem
- </p></dd>
- <dt><span class="term">Coor</span></dt>
- <dd><p>
- The type of the coordinate <span class="emphasis"><em>q</em></span>
- </p></dd>
- <dt><span class="term">MomentumDeriv</span></dt>
- <dd><p>
- The type of the derivative of momentum <span class="emphasis"><em>p'</em></span>
- </p></dd>
- <dt><span class="term">sys</span></dt>
- <dd><p>
- An object that models System
- </p></dd>
- <dt><span class="term">q</span></dt>
- <dd><p>
- Object of type Coor
- </p></dd>
- <dt><span class="term">dpdt</span></dt>
- <dd><p>
- Object of type MomentumDeriv
- </p></dd>
- </dl>
- </div>
- <h5>
- <a name="boost_numeric_odeint.concepts.simple_symplectic_system.h2"></a>
- <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
- 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>
- Check for pair
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_pair</span><span class="special"><</span>
- <span class="identifier">System</span> <span class="special">>::</span><span class="identifier">type</span></code>
- </p>
- </td>
- <td>
- <p>
- <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>
- </p>
- </td>
- <td>
- <p>
- Check if System is a pair, should be evaluated to false in this
- case.
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Calculate <span class="emphasis"><em>dp/dt = g(q)</em></span>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span>
- <span class="identifier">q</span> <span class="special">,</span>
- <span class="identifier">dpdt</span> <span class="special">)</span></code>
- </p>
- </td>
- <td>
- <p>
- <code class="computeroutput"><span class="keyword">void</span></code>
- </p>
- </td>
- <td>
- <p>
- Calculates <span class="emphasis"><em>g(q)</em></span>, the result is stored into
- <code class="computeroutput"><span class="identifier">dpdt</span></code>
- </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 © 2009-2015 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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