204
edits
Toroidal coordinates: Difference between revisions
→Jacobian
| Line 104: | Line 104: | ||
J^{-1} = \det\left(\frac{\partial(\psi,\theta,\phi)}{\partial(x,y,z)}\right) = \nabla{\psi}\cdot\nabla{\theta} \times \nabla{\phi} | J^{-1} = \det\left(\frac{\partial(\psi,\theta,\phi)}{\partial(x,y,z)}\right) = \nabla{\psi}\cdot\nabla{\theta} \times \nabla{\phi} | ||
</math> | </math> | ||
It can be seen that<ref> | It can be seen that <ref></ref> <math>g \equiv \det(g_{ij}) = J^2 \Rightarrow J = \sqrt{g}</math> | ||
== Flux Coordinates == | == Flux Coordinates == | ||