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Geometry > Coordinate Geometry >
Bispherical Coordinates
THINGS TO TRY: 6-sphere coordinates arccot x cbrt(3)
A system of curvilinear coordinates variously denoted (Arfken 1970) or 1988). Using the notation of Arfken, the bispherical coordinates are defined by
(Moon and Spencer (1) (2) (3)
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13,121 entries Last updated: M on Jul 2 2012
Created, developed, and nurtured by Eric Weisstein at Wolfram Research
Surfaces of constant
are given by the spheres (4)
surfaces of constant
by the apples (
) or lemons (
) (5)
and surface of constant
by the half-planes (6)
The scale factors are (7) (8) (9)
The Laplacian is given by (10)
In bispherical coordinates, Laplace's equation is separable (Moon and Spencer 1988), but the Helmholtz differential equation is not.
SEE ALSO:
Bicyclide Coordinates, Laplace's Equation--Bispherical Coordinates, Spherical Coordinates, Toroidal Coordinates
REFERENCES: Arfken, G. "Bispherical Coordinates pp. 115-117, 1970.
." 2.14 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press,
." Fig. 4.03 in Field Theory Handbook, Including Coordinate Systems, Moon, P. and Spencer, D. E. "Bispherical Coordinates Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, pp. 110-112, 1988. Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 665-666, 1953.
Referenced on Wolfram|Alpha: Bispherical Coordinates
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Bispherical Coordinates -- from Wolfram MathWorld
http://mathworld.wolfram.com/BisphericalCoordin...
CITE THIS AS: Weisstein, Eric W. "Bispherical Coordinates." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com /BisphericalCoordinates.html
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