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<p>File containing the angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system.  
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;cmath&gt;</code><br />
<code>#include &lt;string_view&gt;</code><br />
<code>#include &quot;<a class="el" href="equations_2contributions_8hpp.html">serif/equations/contributions.hpp</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="point_8hpp.html">serif/equations/point.hpp</a>&quot;</code><br />
<code>#include &quot;<a class="el" href="rigid__rotation_8hpp.html">serif/equations/rigid_rotation.hpp</a>&quot;</code><br />
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classserif_1_1equations_1_1_angular_momentum_constraint.html">serif::equations::AngularMomentumConstraint</a></td></tr>
<tr class="memdesc:"><td class="mdescLeft">&#160;</td><td class="mdescRight">Angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system.  <a href="classserif_1_1equations_1_1_angular_momentum_constraint.html#details">More...</a><br /></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceserif.html">serif</a></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceserif_1_1equations.html">serif::equations</a></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>File containing the angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system. </p>
<dl class="section author"><dt>Author</dt><dd>Emily M. Boudreaux</dd></dl>
<dl class="section note"><dt>Note</dt><dd>The angular momentum constraint is a global constraint that is enforced by integrating the point-wise contributions of the angular momentum density over the entire domain. The integrand is given by \( j_\parallel = \rho \Omega s^2\), where \(s^2 = |\hat{n} × (r − r_{c})|^2\) is the cylindrical radius squared, and \(\hat{n}\) is the unit rotation axis. The solver will integrate this over the domain and compare it to the target angular momentum to enforce the constraint.</dd></dl>
<p>A few important notes about the implementation</p>
<ul>
<li>The way the equation system plugs into the mfem backend is such that equations should only ever return point wise contributions to the residual, not a global integrated residual. This is why we return \( j_\parallel = \rho \Omega s^2\) as the residual, rather than \( j_\parallel - J_{\text{target}}\). However we still need to subtract the target angular momentum from the integrated residual to enforce the constraint. This is done by implementing the method ::residual_offset() which returns \( -J_{\text{target}}\). The backend will automatically detect and, if present, subtract this from the integrated residual to enforce the constraint.</li>
<li>The solver can choose to validate the angular momentum constraint by integrating the ::validation_integrand() over the domain and then passing this result to ::validate_integral(double result). Note that this is not specific to this equation but a feature of the overall system </li>
</ul>
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