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Flux coordinates: Difference between revisions
→Coordinates and basis vectors
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= \sqrt{g}\;\mathbf{e}^j\times\mathbf{e}^k ~, | = \sqrt{g}\;\mathbf{e}^j\times\mathbf{e}^k ~, | ||
</math> | </math> | ||
where <math>(i,j,k)</math> are cyclic permutations of <math>(1,2,3)</math> and we have used the notation <math>(u^1, u^2, u^3) = (\psi,\theta,\phi)</math>. The Jacobian <math>\sqrt{g}</math> is defined below. | where <math>(i,j,k)</math> are cyclic permutations of <math>(1,2,3)</math> and we have used the notation <math>(u^1, u^2, u^3) = (\psi,\theta,\phi)</math>. The Jacobian <math>\sqrt{g}</math> is defined below. Similarly | ||
:<math> | |||
\mathbf{e}^i = \frac{\mathbf{e}_j\times\mathbf{e}_k}{\sqrt{g}} ~. | |||
</math> | |||
Any vector field <math>\mathbf{B}</math> can be represented as | Any vector field <math>\mathbf{B}</math> can be represented as | ||