Flux coordinates: Difference between revisions
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→Some surface elements
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=== Some surface elements === | === Some surface elements === | ||
Consider a surface defined by a constant value of <math>\phi</math>. Then, the surface element is | |||
:<math> | :<math> | ||
d{\mathbf S}_\phi = \mathbf{e}_\psi\times\mathbf{e}_\theta d\psi d\theta | d{\mathbf S}_\phi = \mathbf{e}_\psi\times\mathbf{e}_\theta d\psi d\theta = \sqrt{g}\nabla\phi d\psi d\theta . | ||
</math> | </math> | ||
As for a surface defined by a constant value of <math>\theta</math>: | As for a surface defined by a constant value of <math>\theta</math>: | ||
:<math> | :<math> | ||
d{\mathbf S}_\theta = \mathbf{e}_\phi\times\mathbf{e}_\psi d\psi d\phi. | d{\mathbf S}_\theta = \mathbf{e}_\phi\times\mathbf{e}_\psi d\psi d\phi = \sqrt{g}\nabla\theta d\psi d\phi . | ||
</math> | </math> | ||
=== Gradient, Divergence and Curl in curvilinear coordinates === | === Gradient, Divergence and Curl in curvilinear coordinates === | ||