2022•arXiv (Cornell University)Open access

Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation

Pavel Strunz

Abstract

The unit vectors transformation between the Cartesian and the novel Similar Oblate Spheroidal coordinates, and vice versa, is derived. It can help to transform vector fields between these two types of orthogonal coordinates which can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in Similar Oblate Spheroidal coordinate system are introduced.

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Key concepts: Orthogonal coordinates, Prolate spheroidal coordinates, Bipolar coordinates, Oblate spheroid, Cartesian coordinate system, Log-polar coordinates, Elliptic coordinate system, Sine