Analytical solution of orthogonal similar oblate spheroidal coordinate system

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00563463" target="_blank" >RIV/61389005:_____/22:00563463 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s10569-022-10099-z" target="_blank" >https://doi.org/10.1007/s10569-022-10099-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s10569-022-10099-z" target="_blank" >10.1007/s10569-022-10099-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analytical solution of orthogonal similar oblate spheroidal coordinate system

Popis výsledku v původním jazyce

Satisfactory description of gravitational and gravity potential is needed for a proper modelling of a wide spectrum of physical problems on various size scales, ranging from atmosphere dynamics up to the movement of stars in a galaxy. The presented orthogonal similar oblate spheroidal (SOS) coordinate system can be a modelling tool applicable for a broad variety of objects exhibiting density, gravity or gravitation potential levels resembling similar oblate spheroids. This can be the case inside or in the vicinity of various oblate spheroidal objects (planets, stars, elliptical galaxies, disk galaxies) exhibiting broad range of oblateness. Although the solution of the relevant expressions for the SOS system cannot be written in a closed form, they are derived as analytical expressions-convergent infinite power series employing generalized binomial coefficients. Transformations of SOS coordinates to and from the Cartesian coordinates are shown. The corresponding partial derivatives are found in a suitable form, further enabling derivation of the metric scale factors necessary for differential operations. The terms containing derivatives of the metric scale factors in the velocity advection term of the momentum equation in the SOS coordinate system are expressed. The Jacobian determinant is derived as well.

Název v anglickém jazyce

Analytical solution of orthogonal similar oblate spheroidal coordinate system

Popis výsledku anglicky

Satisfactory description of gravitational and gravity potential is needed for a proper modelling of a wide spectrum of physical problems on various size scales, ranging from atmosphere dynamics up to the movement of stars in a galaxy. The presented orthogonal similar oblate spheroidal (SOS) coordinate system can be a modelling tool applicable for a broad variety of objects exhibiting density, gravity or gravitation potential levels resembling similar oblate spheroids. This can be the case inside or in the vicinity of various oblate spheroidal objects (planets, stars, elliptical galaxies, disk galaxies) exhibiting broad range of oblateness. Although the solution of the relevant expressions for the SOS system cannot be written in a closed form, they are derived as analytical expressions-convergent infinite power series employing generalized binomial coefficients. Transformations of SOS coordinates to and from the Cartesian coordinates are shown. The corresponding partial derivatives are found in a suitable form, further enabling derivation of the metric scale factors necessary for differential operations. The terms containing derivatives of the metric scale factors in the velocity advection term of the momentum equation in the SOS coordinate system are expressed. The Jacobian determinant is derived as well.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Celestial Mechanics and Dynamical Astronomy

ISSN

0923-2958

e-ISSN

1572-9478

Svazek periodika

134

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

39

Strana od-do

51

Kód UT WoS článku

000869844200002

EID výsledku v databázi Scopus

2-s2.0-85140229812