Mathematics
Scientific paper
Mar 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..32..257s&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 32, March 1984, p. 257-296.
Mathematics
13
Geodesy, Gravitational Fields, Inertia, Tensors, Cartesian Coordinates, Matrices (Mathematics), Spherical Harmonics
Scientific paper
A novel tensor-matrix notation is used in developing a new general expression for computing the potential of a body at exterior points as function of the full tensors of inertia. It is noted that the final expressions are original in the sense that they depend exclusively on two major parameters: the Cartesian coordinates of the point and a set of inertial tensors of the body. The theory is developed in a general matrix form introduced through a novel notation that make use of basic matrix algebra operations. Certain applications of the general equations are obtained and discussed, and simple formulas for the first terms of the expansion are arrived at. These are easy to visualize and comprehend without the aid of laborious and lengthy polynomial expressions.
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