Comparison of main geometric characteristics of deformed sphere and standard spheroid

• Autorzy: Kovalchuk Vasyl , Mladenov Ivaïlo M.

Identyfikatory

DOI

10.24425/bpasts.2023.147058

• Języki publikacji: EN

Abstrakty

EN

In the paper we compare the geometric descriptions of the deformed sphere (i.e., the so-called λ-sphere) and the standard spheroid (namely, World Geodetic System 1984’s reference ellipsoid of revolution). Among the main geometric characteristics of those two surfaces of revolution embedded into the three-dimensional Euclidean space we consider the semi-major (equatorial) and semi-minor (polar) axes, quartermeridian length, surface area, volume, sphericity index, and tipping (bifurcation) point for geodesics. Next, the RMS (Root Mean Square) error is defined as the square-rooted arithmetic mean of the squared relative errors for the individual pairs of the discussed six main geometric characteristics. As a result of the process of minimization of the RMS error, we have obtained the proposition of the optimized value of the deformation parameter of the λ-sphere, for which we have calculated the absolute and relative errors for the individual pairs of the discussed main geometric characteristics of λ-sphere and standard spheroid (the relative errors are of the order of 10−6 – 10−9). Among others, it turns out that the value of the,sup> flattening factor of the spheroid is quite a good approximation for the corresponding value of the deformation parameter of the λ-sphere (the relative error is of the order of 10−4).

Słowa kluczowe

EN

deformed sphere; standard spheroid; sphericity index; elliptic integrals; elliptic functions; tipping point; bifurcation point

PL

sfera zdeformowana; sferoida standardowa; współczynnik sferyczności; punkt zwrotny; punkt bifurkacji; całka eliptyczna; funkcja eliptyczna

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2023
• Tom: Vol. 71, nr 5
• Strony: art. no. e147058
• Opis fizyczny: Bibliogr. 19 poz., rys., tab.

Twórcy

autor

Kovalchuk Vasyl

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland

• https://orcid.org/0000-0001-5391-2706

autor

Mladenov Ivaïlo M.

• Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
• Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria

• https://orcid.org/0000-0001-5577-5741

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).