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I want to use Vector Analysis functions (Grad, Div,Curl etc) with the following set of simple Toroidal coordinates $(r, \theta, \phi)$:

$x = (R+r \cos\theta)\sin\phi$, $y = (R+r \cos\theta)\cos\phi$, $z = r \sin\theta$

I already have the scale factors and all that, and I am aware there is already a set of toroidal coordinates coded into the built in function, but they are different from mine. Is there any way to code my own system of coordinates to later use with Grad, Div etc..? Thanks

user64494
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Javier Chico
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  • All that can be realized in Maple. For example, with(VectorCalculus): SetCoordinates('toroidal'[r, theta, phi]): V := VectorField(<,>(r^2, sin(theta), cos(phi))); Curl(V); – user64494 Oct 12 '23 at 18:23
  • I have not verified the formulas, but maybe you can use the general formulas found here https://en.wikipedia.org/wiki/Orthogonal_coordinates#Differential_operators_in_three_dimensions – userrandrand Oct 12 '23 at 22:03
  • Also, I did not try it but, https://mathematica.stackexchange.com/a/47903/86543 mentions a package that might help or do this – userrandrand Oct 12 '23 at 22:10
  • Another package that is quite old and I do not know if it still works or helps https://library.wolfram.com/infocenter/MathSource/709/ – userrandrand Oct 12 '23 at 22:13
  • Look at: CoordinateTransformData[] and TransformedField. – Syed Oct 13 '23 at 01:36

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