Convergence of Liapunov Series for Maclaurin Ellipsoids: Real Analysis

Author: Kholshevnikov, Konstantin V.

Source: Celestial Mechanics and Dynamical Astronomy, Volume 87, Number 3, November 2003 , pp. 257-262(6)

Publisher: Springer

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Abstract:

According to the classical theory of equilibrium figures, surfaces of equal density, potential and pressure concur (let us call them isobars). Isobars can be represented by means of Liapunov power series in a small parameter q, in the first approximation coinciding with the centrifugal to gravitational force ratio at the equator. In [5] the convergence radius for Liapunov series was found in case of homogeneous equilibrium figures (Maclaurin ellipsoids). Isobars were described by means of implicit functions of q. The proof was based on the analysis of these functions in a complex domain and used computer algebra tools. Here we present a much simpler proof examining the above mentioned functions in a real domain only.

Keywords: Liapunov series; Maclaurin ellipsoids; convergence radius; figures of equilibrium

Document Type: Research Article

Affiliations: Astronomical Institute of St. Petersburg University, Universitetsky pr. 28 Stary Peterhof, 198504 St. Petersburg, Russia

Publication date: November 1, 2003

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