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| <div class="section"> |
| <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> |
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| <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>) |
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