Analytical solution of orthogonal similar oblate spheroidal coordinate system
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Analytical solution of orthogonal similar oblate spheroidal coordinate system
Original language description
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.
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
10308 - Astronomy (including astrophysics,space science)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Celestial Mechanics and Dynamical Astronomy
ISSN
0923-2958
e-ISSN
1572-9478
Volume of the periodical
134
Issue of the periodical within the volume
6
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
39
Pages from-to
51
UT code for WoS article
000869844200002
EID of the result in the Scopus database
2-s2.0-85140229812