| 释义 |
Parabolic CoordinatesA system of Curvilinear Coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolasof Parabolic Cylindrical Coordinates about the x-Axis, which is then relabeled the z-Axis. Thereare several notational conventions. Whereas  is used in this work, Arfken (1970) uses  .
The equations for the parabolic coordinates are
where  ,  , and  . To solve for  ,  , and  , examine
so
 | (5) |
 | (6) |
 | (7) |
The Scale Factors are
The Line Element is
 | (14) |
 | (15) |
The Helmholtz Differential Equation is Separable in parabolic coordinates.See also Confocal Paraboloidal Coordinates, Helmholtz Differential Equation--Parabolic Coordinates, Parabolic Cylindrical Coordinates
References
Arfken, G. ``Parabolic Coordinates ( ,  ,  ).'' §2.12 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 109-112, 1970.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 660, 1953.
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