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Oblate and prolate spheroidal coordinates
Journal article   Peer reviewed

Oblate and prolate spheroidal coordinates

Bi-Trong Chen and Sanboh Lee
Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering, Vol.22(5), pp.563-566
09/1998

Abstract

We propose that the transformation equations from cartesian coordinates (x,y,z) to oblate spheroidal coordinates (u,ν,φ) are x = f csc u sin ν cos φ, y = f csc u sin ν sin φ, and z = f cot u cos ν, where f is the half focal length. The transformation equations from cartesian coordinates to prolate spheroidal coordinates can be obtained from the above expressions if u and f are replaced by iu and if, respectively, where i = √-1. Any function and its derivatives in oblate spheroidal coordinates can be also transformed into prolate spheroidal coordinates if u and f in oblate spheroidal coordinates are replaced by iu and if, respectively.

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