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

单词

Toroidal Coordinates

释义

Toroidal Coordinates

A system of Curvilinear Coordinates for which several different notations are commonly used. In this work(, , ) is used, whereas Arfken (1970) uses (, , ). The toroidal coordinates aredefined by

			(1)
			(2)
			(3)

where

is the Hyperbolic Sine and

is the Hyperbolic Cosine.The Scale Factors are

			(4)
			(5)
			(6)

The Laplacian is


	(7)

	(8)

The Helmholtz Differential Equation is not separable in toroidal coordinates, but Laplace's Equation is.

See also Bispherical Coordinates, Laplace's Equation--Toroidal Coordinates

References

Arfken, G. ``Toroidal Coordinates (, , ).'' §2.13 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 112-115, 1970.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 666, 1953.

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