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

单词

Conical Coordinates

释义

Conical Coordinates

Arfken (1970) and Morse and Feshbach (1953) use slightly different definitions of these coordinates.The system used in Mathematica (Wolfram Research, Inc., Champaign, Illinois) is

			(1)
			(2)
			(3)

where

. The Notation of Byerly replaces

with

, and

and

with

and

.The above equations give

(4)

(5)

(6)

The Scale Factors are

			(7)
			(8)
			(9)

The Laplacian is


	(10)

The Helmholtz Differential Equation is separable in conical coordinates.

See also Helmholtz Differential Equation--Conical Coordinates

References

Arfken, G. ``Conical Coordinates (, , ).'' §2.16 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 118-119, 1970.

Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, p. 263, 1959.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 659, 1953.

Spence, R. D. ``Angular Momentum in Sphero-Conal Coordinates.'' Amer. J. Phys. 27, 329-335, 1959.

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