Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation
Pavel Strunz
TL;DR
This paper derives the transformation of unit vectors between Cartesian and a new Similar Oblate Spheroidal coordinate system, facilitating easier vector field analysis in oblate spheroidal geometries with practical examples.
Contribution
It introduces the transformation relations for unit vectors between Cartesian and Similar Oblate Spheroidal coordinates, including generalized trigonometric functions, enhancing problem-solving in spheroidal geometries.
Findings
Derived unit vector transformation formulas.
Presented examples demonstrating the application.
Introduced generalized sine and cosine functions.
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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Taxonomy
TopicsStatistical and numerical algorithms · Inertial Sensor and Navigation · Aerospace Engineering and Control Systems