\doxysection{src/include/serif/equations/angular\+\_\+momentum.hpp File Reference}
\hypertarget{angular__momentum_8hpp}{}\label{angular__momentum_8hpp}\index{src/include/serif/equations/angular\_momentum.hpp@{src/include/serif/equations/angular\_momentum.hpp}}


File containing the angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system.  


{\ttfamily \#include $<$cmath$>$}\newline
{\ttfamily \#include $<$string\+\_\+view$>$}\newline
{\ttfamily \#include "{}serif/equations/contributions.\+hpp"{}}\newline
{\ttfamily \#include "{}serif/equations/point.\+hpp"{}}\newline
{\ttfamily \#include "{}serif/equations/rigid\+\_\+rotation.\+hpp"{}}\newline
Include dependency graph for angular\+\_\+momentum.\+hpp\+:
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This graph shows which files directly or indirectly include this file\+:
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\includegraphics[width=350pt]{angular__momentum_8hpp__dep__incl}
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\doxysubsubsection*{Classes}
\begin{DoxyCompactItemize}
\item 
class \mbox{\hyperlink{classserif_1_1equations_1_1_angular_momentum_constraint}{serif\+::equations\+::\+Angular\+Momentum\+Constraint}}
\begin{DoxyCompactList}\small\item\em Angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system. \end{DoxyCompactList}\end{DoxyCompactItemize}
\doxysubsubsection*{Namespaces}
\begin{DoxyCompactItemize}
\item 
namespace \mbox{\hyperlink{namespaceserif}{serif}}
\item 
namespace \mbox{\hyperlink{namespaceserif_1_1equations}{serif\+::equations}}
\end{DoxyCompactItemize}


\doxysubsection{Detailed Description}
File containing the angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system. 

\begin{DoxyAuthor}{Author}
Emily M. Boudreaux
\end{DoxyAuthor}


\begin{DoxyNote}{Note}
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.
\end{DoxyNote}
A few important notes about the implementation


\begin{DoxyItemize}
\item 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.
\item 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 
\end{DoxyItemize}