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Toroidal coordinates: Difference between revisions
→Jacobian
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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></center> | </math></center> | ||
It can be seen that <math>g \equiv \det(g_{ij}) = J^2 \Rightarrow J = \sqrt{g}</math> | It can be seen that<ref>W.D. D'haeseleer, ''Flux coordinates and magnetic field structure: a guide to a fundamental tool of plasma theory'', Springer series in computational physics, Springer-Verlag (1991) ISBN 3540524193</ref> <math>g \equiv \det(g_{ij}) = J^2 \Rightarrow J = \sqrt{g}</math> | ||
== Magnetic == | == Magnetic == | ||