Flux coordinates: Difference between revisions
→General curvilinear coordinates
| Line 63: | Line 63: | ||
</math> | </math> | ||
It can be seen that <ref name='Dhaeseleer'></ref> <math>g \equiv \det(g_{ij}) = J^2 \Rightarrow J = \sqrt{g}</math> | It can be seen that <ref name='Dhaeseleer'></ref> <math>g \equiv \det(g_{ij}) = J^2 \Rightarrow J = \sqrt{g}</math> | ||
=== Some surface elements === | |||
Let <math>S_\phi</math> a surface defined by a constant value of <math>\phi</math>. Then, the surface element is | |||
:<math> | |||
d{\mathbf S}_\phi = \mathbf{e}_\psi\times\mathbf{e}_\theta\d\psi d\theta | |||
</math> | |||
=== Gradient, Divergence and Curl in curvilinear coordinates === | === Gradient, Divergence and Curl in curvilinear coordinates === | ||