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Toroidal coordinates: Difference between revisions
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where ''R<sub>p</sub>'' is the pole of the coordinate system. | where ''R<sub>p</sub>'' is the pole of the coordinate system. | ||
Surfaces of constant ''ζ'' are tori with major radii ''R = R<sub>p</sub>''/tanh ''ζ'' and minor radii ''r = R<sub>p</sub>''/sinh ''ζ''. | Surfaces of constant ''ζ'' are tori with major radii ''R = R<sub>p</sub>''/tanh ''ζ'' and minor radii ''r = R<sub>p</sub>''/sinh ''ζ''. | ||
At ''R = R<sub>p</sub>'', ''ζ'' = | At ''R = R<sub>p</sub>'', ''ζ'' = ∞, while at infinity and at ''R = 0, ζ = 0''. | ||
The coordinate ''η'' is a poloidal angle and runs from 0 to 2π. | The coordinate ''η'' is a poloidal angle and runs from 0 to 2π. | ||
This system is orthogonal. | This system is orthogonal. | ||