Invariant vector harmonics. The ellipsoidal case

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Dassios, George¹  Vafeas, Panayiotis² 

[1] Univ Patras, Dept Chem Engn, GR-26110 Patras, Greece

[2] Univ Patras, Dept Engn Sci, GR-26110 Patras, Greece

关键词: Vector harmonics;    Spherical harmonics;    Ellipsoidal harmonics;   

DOI  :  10.1016/j.jmaa.2013.03.015

来源: Elsevier

【 摘 要 】

We introduce a complete set of vector harmonic functions in an invariant form, that is, in a form that is independent of any coordinate system. In fact, we define three vector differential operators of the first order which, when they act on a scalar harmonic function they generate three independent vector harmonic functions. Then, we prove the relative independence properties and we investigate the characterization of every harmonic as an irrotational or solenoidal field. We also prove that this set of functions forms a complete set of vector harmonics. Finally, we use these invariant expressions to recover the vector spherical harmonics of Hansen and to introduce vector ellipsoidal harmonics in R-3. Our method can be applied to any other coordinate system to produce the corresponding vector harmonics. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free