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Toroidal coordinates

From Encyclopedia of Mathematics
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The numbers , and related to the Cartesian rectangular coordinates , and by the formulas:

where , , . The coordinate surfaces are spheres with centre and radius ; the surfaces are tori with axial circle in the -plane, centre at the origin and radius , while the circle of the transverse cross section has radius ; the surfaces are the half-planes . The system of toroidal coordinates is orthogonal.

The Lamé coefficients are:

The Laplace operator is:

How to Cite This Entry:
Toroidal coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Toroidal_coordinates&oldid=15155
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article