On Laplace Equation Solution in Orthogonal Similar Oblate Spheroidal Coordinates

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F25%3A00619376" target="_blank" >RIV/61389005:_____/25:00619376 - isvavai.cz</a>

Výsledek na webu

<a href="https://ojs.wiserpub.com/index.php/CM/article/view/4965" target="_blank" >https://ojs.wiserpub.com/index.php/CM/article/view/4965</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.37256/cm.6220254965" target="_blank" >10.37256/cm.6220254965</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Laplace Equation Solution in Orthogonal Similar Oblate Spheroidal Coordinates

Popis výsledku v původním jazyce

Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies or particles with the geometry of an oblate spheroid. The interior solution of the Laplace equation in the SOS coordinates was recently found, however, the exterior solution was missing. The exterior solution of the azimuthally symmetric Laplace equation in the SOS coordinates is derived. In the steps leading to this solution, important formulas of the SOS algebra are found. Various forms of the Laplace operator in the SOS coordinates in azimuthally symmetric case are shown. General transformation between two different SOS coordinate systems is derived. It is determined that the SOS harmonics are physically the same as the solid harmonics. Further, a formula expressing any generalized Legendre polynomial as a finite sum of monomials is found. The reported relations have potential application in geophysics, astrophysics, electrostatics, electromagnetism, fluid flow and solid state physics (e.g., ferroic inclusions).

Název v anglickém jazyce

On Laplace Equation Solution in Orthogonal Similar Oblate Spheroidal Coordinates

Popis výsledku anglicky

Orthogonal coordinate systems enable expressing the boundary conditions of differential equations in accord with the physical boundaries of the problem. It can significantly simplify calculations. The orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies or particles with the geometry of an oblate spheroid. The interior solution of the Laplace equation in the SOS coordinates was recently found, however, the exterior solution was missing. The exterior solution of the azimuthally symmetric Laplace equation in the SOS coordinates is derived. In the steps leading to this solution, important formulas of the SOS algebra are found. Various forms of the Laplace operator in the SOS coordinates in azimuthally symmetric case are shown. General transformation between two different SOS coordinate systems is derived. It is determined that the SOS harmonics are physically the same as the solid harmonics. Further, a formula expressing any generalized Legendre polynomial as a finite sum of monomials is found. The reported relations have potential application in geophysics, astrophysics, electrostatics, electromagnetism, fluid flow and solid state physics (e.g., ferroic inclusions).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EH22_008%2F0004591" target="_blank" >EH22_008/0004591: Feroické multifunkcionality</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Contemporary Mathematics

ISSN

2705-1064

e-ISSN

2705-1056

Svazek periodika

6

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

23

Strana od-do

1715-1737

Kód UT WoS článku

001471434300022

EID výsledku v databázi Scopus

2-s2.0-105000327133