Partial separability of the Laplace equation in Roche coordinates

Details Partial separability of the Laplace equation in Roche coordinates Partial separability of the Laplace equation in Roche coordinates

Feb 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979ap%26ss..60..431l&link_type=abstract

Astrophysics and Space Science, vol. 60, no. 2, Feb. 1979, p. 431-439.

Astronomy and Astrophysics

Astrophysics

1

Astronomical Coordinates, Astrophysics, Laplace Equation, Roche Limit, Orthogonality, Partial Differential Equations, Vector Analysis

Scientific paper

This paper considers the separability of the Laplace equation with respect to the distinguished coordinate in a semiorthogonal coordinate system where two of the families of coordinate surfaces are orthogonal to the third but not necessarily to each other. If the surfaces v = const and w = const are each orthogonal to u = const, solutions to the Laplace equation of the form F(u)G(v, w) are sought; the equation is referred to as u-separable if there is separability of this type. It is shown that the Laplace equation is not u-separable in semiorthogonal Roche coordinates for the rotation problem if the functions v and w are analytic in the parameter n and the coordinate system is proper in an interval where n lies between zero and some value nzero, and also that the same equation remains non-u-separable in the general semiorthogonal Roche coordinate case if F1G2-F2G1 is not identically equal to zero.

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