Een coördinaatvrije basis voor vectorvelden in de context van rotatiesymmetrische operatoren met behulp van sferisch harmonische functies

Een coördinaatvrije basis voor vectorvelden in de context van rotatiesymmetrische operatoren met behulp van sferisch harmonische functies

Fleuren, Jules (TU Delft Electrical Engineering, Mathematics and Computer Science)

van der Toorn, R. (mentor)
Janssens, B. (graduation committee)

Delft University of Technology

Applied Mathematics

2021-07-07

Vector spherical harmonics are a set of basis functions for vector fields derived from the spherical harmonic functions. They are commonly used in spectral methods in certain areas of applied mathematics. In most of the existing literature they are defined in a way that is heavily dependent on the used coördinate system. In this thesis we define vector spherical harmonics in a coördinate free manner. We first do this on a sphere, using two tensor operators: the exterior derivative and the Hodge-star. We then extend these functions to vector functions in 3-dimensional Euclidian space and define a last type of vector function to form a complete basis for vector fields. We do this in such a manner that the vector spherical harmonics inherit some of the nice properties of the spherical harmonic functions with respect to rotations and rotational symmetric operators.

Coordinate free
Spherical harmonics
vector spherical harmonics
rotational symmetries

http://resolver.tudelft.nl/uuid:8579b912-508f-467b-a551-d40bd720da8e

Student theses

bachelor thesis

© 2021 Jules Fleuren