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

单词

Parabolic Cylindrical Coordinates

释义

Parabolic Cylindrical Coordinates

A system of Curvilinear Coordinates. There are several different conventions for the orientation and designation ofthese coordinates. Arfken (1970) defines coordinates such that

			(1)
			(2)
			(3)

In this work, following Morse and Feshbach (1953), the coordinates

are used instead. In this convention, thetraces of the coordinate surfaces of the

-Plane are confocal Parabolas with a common axis. The

curves open into the Negative x-Axis; the

curves open into the Positive x-Axis. The

and

curves intersect along the y-Axis.

			(4)
			(5)
			(6)

where

, and

. The Scale Factors are

			(7)
			(8)
			(9)

Laplace's Equation is

(10)

The Helmholtz Differential Equation is Separable in parabolic cylindricalcoordinates.

See also Confocal Paraboloidal Coordinates, Helmholtz Differential Equation--Parabolic CylindricalCoordinates, Parabolic Coordinates

References

Arfken, G. ``Parabolic Cylinder Coordinates (, , ).'' §2.8 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, p. 97, 1970.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 658, 1953.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。