Flux coordinates: Difference between revisions
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=== Coordinates and basis vectors === | === Coordinates and basis vectors === | ||
Let <math>{\mathbf x}</math> be a set of euclidean coordinates on <math>{\mathbb R}^3</math> | Let <math>{\mathbf x}</math> be a set of euclidean coordinates on <math>{\mathbb R}^3</math> and let <math>(\psi(\mathbf{x}),\theta(\mathbf{x}),\phi(\mathbf{x}))</math> define a change of coordinates, arbitrary for the time being. | ||
We can calculate the contravariant basis vectors as | |||
:<math> | :<math> | ||
\mathbf{e}^i = \{\nabla\psi, \nabla\theta, \nabla\phi\} | \mathbf{e}^i = \{\nabla\psi, \nabla\theta, \nabla\phi\} | ||