SpECTRE
v2024.05.11
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Tangents(i,j)
is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. CartesianCoords
) and are considered functions of \((\theta,\phi)\).
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#include <Tags.hpp>
Public Types | |
using | type = aliases::Jacobian< Frame > |
Tangents(i,j)
is \(\partial x_{\rm surf}^i/\partial q^j\), where \(x_{\rm surf}^i\) are the Cartesian coordinates of the surface (i.e. CartesianCoords
) and are considered functions of \((\theta,\phi)\).
\(\partial/\partial q^0\) means \(\partial/\partial\theta\); and \(\partial/\partial q^1\) means \(\csc\theta\,\,\partial/\partial\phi\). Note that the vectors Tangents(i,0)
and Tangents(i,1)
are orthogonal to the NormalOneForm
\(s_i\), i.e. \(s_i \partial x_{\rm surf}^i/\partial q^j = 0\); this statement is independent of a metric. Also, Tangents(i,0)
and Tangents(i,1)
are not necessarily orthogonal to each other, since orthogonality between 2 vectors (as opposed to a vector and a one-form) is metric-dependent.