.TH "src/include/serif/equations/angular_momentum.hpp" 3 "Version v0.0.1a" "SERiF" \" -*- nroff -*-
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.SH NAME
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\&.  

.SH SYNOPSIS
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.PP
\fR#include <cmath>\fP
.br
\fR#include <string_view>\fP
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\fR#include 'serif/equations/contributions\&.hpp'\fP
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\fR#include 'serif/equations/point\&.hpp'\fP
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\fR#include 'serif/equations/rigid_rotation\&.hpp'\fP
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.SS "Classes"

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.ti -1c
.RI "class \fBserif::equations::AngularMomentumConstraint\fP"
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.RI "Angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system\&. "
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.SS "Namespaces"

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.RI "namespace \fBserif\fP"
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.RI "namespace \fBserif::equations\fP"
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.SH "Detailed Description"
.PP 
File containing the angular momentum constraint equation, which enforces a global constraint on the total angular momentum of a system\&. 


.PP
\fBAuthor\fP
.RS 4
Emily M\&. Boudreaux
.RE
.PP

.PP
\fBNote\fP
.RS 4
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\&.
.RE
.PP
A few important notes about the implementation

.PP
.IP "\(bu" 2
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\&.
.IP "\(bu" 2
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 
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for SERiF from the source code\&.