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The Ultimate Image Singularities for External Spheroidal and Ellipsoidal Harmonics

Author: Miloh, T.
Contributor: Landweber, L.
Publisher: University of Iowa
Source:Iowa Institute of Hydraulic Research
Keywords: spheroid · ellipsoid · image singularities · singularities · hydrodynamic · fluid mechanics
Classification: TLJ800400
Origin:TU Delft
Rights: (c) 1973 University of Iowa · Miloh, T.


The image system of singularities of an arbitrary exterior potential field within a tri-axial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field with in a sphere and spheroid. A proof of Havelock's spheroid theorem which apparently is not available in the literature is also given. The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem.
The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation.

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