Ellipsoidal potentials of polynomial distributions of matter

Details Ellipsoidal potentials of polynomial distributions of matter Ellipsoidal potentials of polynomial distributions of matter

Dec 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979apj...234..619l&link_type=abstract

Astrophysical Journal, Part 1, vol. 234, Dec. 1, 1979, p. 619-627.

Astronomy and Astrophysics

Astrophysics

7

Computer Techniques, Density Distribution, Ellipsoids, Gravitation Theory, Polynomials, Potential Theory, Algorithms, Cartesian Coordinates, Data Processing, Stellar Rotation, Symbols

Scientific paper

Ferrer's method for calculating the potential in the interior of an ellipsoid, due to matter occupying that ellipsoid and having a density represented by a polynomial function of the Cartesian coordinates, is organized into algorithmic form usable for polynomials of arbitrary degree, and adapted for symbol manipulation by computer. A systematic notation is introduced for coefficients appearing in this algorithm, and identities among these coefficients are derived which generalize and clarify sets of identities that have previously been used. More important, identities among the potentials due to monomial density functions are derived which not only simplify their calculation but also play a theoretical role in their application to the theory of self-gravitating masses.

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