Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00586597" target="_blank" >RIV/61389005:_____/24:00586597 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1140/epjp/s13360-024-05181-4" target="_blank" >https://doi.org/10.1140/epjp/s13360-024-05181-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-024-05181-4" target="_blank" >10.1140/epjp/s13360-024-05181-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Popis výsledku v původním jazyce

Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably simple way when the coordinate surfaces fit the physical boundaries of the problem. The recently finalized 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 solution of the azimuthally symmetric case of the Laplace equation was found for the interior space in the orthogonal SOS coordinates. In the frame of the derivation of the harmonic functions, the Laplace equation was separated by a special separation procedure. A generalized Legendre equation was introduced as the equation for the angular part of the separated Laplace equation. The harmonic functions were determined as relations involving generalized Legendre functions of the first and of the second kind. Several lower-degree functions are reported. Recursion formula facilitating determination of the higher-degree harmonic functions was found. The general solution of the azimuthally symmetric Laplace equation for the interior space in the SOS coordinates is reported.

Název v anglickém jazyce

Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Popis výsledku anglicky

Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably simple way when the coordinate surfaces fit the physical boundaries of the problem. The recently finalized 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 solution of the azimuthally symmetric case of the Laplace equation was found for the interior space in the orthogonal SOS coordinates. In the frame of the derivation of the harmonic functions, the Laplace equation was separated by a special separation procedure. A generalized Legendre equation was introduced as the equation for the angular part of the separated Laplace equation. The harmonic functions were determined as relations involving generalized Legendre functions of the first and of the second kind. Several lower-degree functions are reported. Recursion formula facilitating determination of the higher-degree harmonic functions was found. The general solution of the azimuthally symmetric Laplace equation for the interior space in the SOS coordinates is reported.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10304 - Nuclear physics

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

2024

Kód důvěrnosti údajů

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

Název periodika

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

2190-5444

Svazek periodika

139

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

35

Strana od-do

409

Kód UT WoS článku

001222553700002

EID výsledku v databázi Scopus

2-s2.0-85193258109