Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation
arXiv:2204.01474 · doi:10.1007/s00033-023-02058-x
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.
33 pages, 1 figure