Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10304 - Nuclear physics
Result continuities
Project
<a href="/en/project/EH22_008%2F0004591" target="_blank" >EH22_008/0004591: Ferroic Multifunctionalities</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
European Physical Journal Plus
ISSN
2190-5444
e-ISSN
2190-5444
Volume of the periodical
139
Issue of the periodical within the volume
5
Country of publishing house
DE - GERMANY
Number of pages
35
Pages from-to
409
UT code for WoS article
001222553700002
EID of the result in the Scopus database
2-s2.0-85193258109