- Tytuł:
- Comparison of main geometric characteristics of deformed sphere and standard spheroid
- Autorzy:
-
Kovalchuk, Vasyl
Mladenov, Ivaïlo M. - Tematy:
-
deformed sphere
standard spheroid
sphericity index
elliptic integrals
elliptic functions
tipping point
bifurcation point
sfera zdeformowana
sferoida standardowa
współczynnik sferyczności
punkt zwrotny
punkt bifurkacji
całka eliptyczna
funkcja eliptyczna - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Czasopisma i Monografie PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/27311436.pdf Link otwiera się w nowym oknie
- Opis:
- 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).
- Dostawca treści:
- Biblioteka Nauki
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