Flux coordinates: Difference between revisions
→Some surface elements
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Consider a surface defined by a constant value of <math>\phi</math>. Then, the surface element is | 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 = \sqrt{g} \nabla\phi 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 = \sqrt{g} \nabla\theta 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> | ||