Ellipsoids, material points and material segments

Simple models of potential based on material points and material segments are confronted with a homogeneous ellipsoid potential. A spheroid is approximated with a pair of material points or with one material segment. The segment model proves to be more accurate. For a triaxial ellipsoid, two models are considered: one with five material points and one with two material segments and a point. When their parameters are determined with the fourth sectorial harmonic ignored, both simple models have a similar approximation error. Numerical tests indicate that the approximate models of a triaxial ellipsoid are 5 to 10 times faster than exact formulation, whereas for a spheroid the approximate models are at most twice as fast as the exact formulae.