Toroidal coordinates
From Encyclopedia of Mathematics
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=48996
Toroidal coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Toroidal_coordinates&oldid=48996
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article