English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Satisfactory description of gravitational and gravity potentials is neededfor a proper modelling of a wide spectrum of physical problems on various sizescales, ranging from atmosphere dynamics up to the movements of stars in agalaxy. In certain cases, Similar Oblate Spheroidal (SOS) coordinate system canbe of advantage for such modelling tasks, mainly inside or in the vicinity ofoblate spheroidal objects (planets, stars, galaxies). Although the solution ofthe relevant expressions for the SOS system cannot be written in a closed form,it can be derived as analytical expressions -- convergent infinite powerseries. Explicit analytical expressions for the Cartesian coordinates in termsof the curvilinear Similar Oblate Spheroidal coordinates are derived in theform of infinite power series with generalized binomial coefficients. Thecorresponding partial derivatives are found in a suitable form, furtherenabling derivation of the metric scale factors necessary for differentialoperations. The terms containing derivatives of the metric scale factors in thevelocity advection term of the momentum equation in SOS coordinate system areexpressed. The Jacobian determinant is derived as well. The presentedanalytical solution of SOS coordinate system solution is a tool applicable fora broad variety of objects exhibiting density, gravity or gravitation levelsresembling similar oblate spheroids. Such objects range from the bodies withsmall oblateness (the Earth itself on the first place), through ellipticalgalaxies up to significantly flattened objects like disk galaxies.

Analytical Solution of Similar Oblate Spheroidal Coordinate System