Statistics – Computation
Scientific paper
May 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987ap%26ss.133..157k&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 133, no. 1, May 1987, p. 157-175.
Statistics
Computation
6
Computational Astrophysics, Harmonic Functions, Laplace Equation, Roche Limit, Rotating Bodies, Stable Oscillations, Angular Velocity, Cartesian Coordinates, Centrifugal Force, Differential Equations, Legendre Functions, Polar Coordinates
Scientific paper
The aim of the first part of this investigation is to establish the explicit form of the linearized systems of differential equations governing arbitrary oscillations (of amplitudes small enough for their squares and higher powers to be negligible) of the rotating Roche model in Clairaut's coordinates. By solving these equations in a closed form the author proves that this model is incapable of performing such oscillations about equipotential surfaces representing the figures of equilibrium, as soon as the centrifugal force will cause their equilibrium form to depart from a sphere. In the second part of this paper the author sets up the closed forms of the Laplace equation in Clairaut (non-orthogonal) as well as Roche (orthogonal) coordinates associated with the rotating Roche model; and by a construction of their solution establishes successively the explicit forms of the respective harmonic functions associated with such figures.
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