“Oblate Spheroidal Coordinates”的概念、定义、习题解题方法及翻译-数学辞典

单词

Oblate Spheroidal Coordinates

释义

Oblate Spheroidal Coordinates

A system of Curvilinear Coordinates in which two sets of coordinate surfaces are obtained by revolving the curves ofthe Elliptic Cylindrical Coordinates about the y-Axis which is relabeled the z-Axis. The third setof coordinates consists of planes passing through this axis.

			(1)
			(2)
			(3)

where

, and

. Arfken (1970) uses

instead of

. The Scale Factors are

			(4)
			(5)
			(6)

The Laplacian is






	(7)
	(8)

An alternate form useful for ``two-center'' problems is defined by

			(9)
			(10)
			(11)
			(12)

where

, and

. In thesecoordinates,

			(13)
			(14)
			(15)

(Abramowitz and Stegun 1972). The Scale Factors are

			(16)
			(17)
			(18)

and the Laplacian is

(19)

The Helmholtz Differential Equation is separable.

See also Helmholtz Differential Equation--Oblate Spheroidal Coordinates,Latitude, Longitude, Prolate Spheroidal Coordinates, Spherical Coordinates

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Definition of Oblate Spheroidal Coordinates.'' §21.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 752, 1972.

Arfken, G. ``Prolate Spheroidal Coordinates (, , ).'' §2.11 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 107-109, 1970.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 663, 1953.

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