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Systematic derivations of measures of arbitrary ellipsoids. (English)
J. Interdiscip. Math. 14, No. 5-6, 493-506 (2011).
Summary: In this paper, systematic derivations of measures of an arbitrary ellipsoid are presented. The measures include volume, surface area and integral of mean curvature. The derivations are all performed in ellipsoidal coordinates the first time. They are systematic, simple and straightforward, no special techniques are needed. The approach can be easily extended to other measures, such as Willmore energy of an ellipsoid or integrals on segments, and also to other coordinate systems or higher-dimensional problems.
Classification: G35
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