I want to use the dipole coordinate system as defined in this paper: http://arxiv.org/abs/physics/0606044
I see that Mathematica can do all kinds of vector analysis using different kinds of coordinate systems, but the dipole coordinate system does not seem to be included. That's understandable: it's an exotic coordinate system after all.
Is there a way to define a new coordinate system to use and then perform vector analysis on it? I have the scale factors, the Jacobian, and so on from the above article.
This is a general question, but here is my application: I am solving a matrix equation where the key matrix is diagonal in the dipole coordinate system. I could rotate/transform that matrix to spherical coordinates (which would be convenient for other vectors in the equation), but doing so requires a different rotation/transformation at every single point, and it isn't clear to me how to do that, or that it would be any better.