Non-Integrability of the Generalized Two Fixed Centres Problem

Authors: Maciejewski, Andrzej1; Przybylska, Maria2

Source: Celestial Mechanics and Dynamical Astronomy, Volume 89, Number 2, June 2004 , pp. 145-164(20)

Publisher: Springer

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Abstract:

We consider two fixed centres attracting a third body. Each centre is the source of a force field with potential V = −ar −2n , where n is a real number. We prove that this generalization of the classical two fixed centres problem is non-integrable except when n = 0, 1/2, −1 and −2.

Keywords: integrability; two fixed centres problem

Document Type: Research Article

DOI: http://dx.doi.org/10.1023/B:CELE.0000034513.45950.86

Affiliations: 1: Email: maciejka@astro.ia.uz.zgora.pl 2: Email: Maria.Przybylska@sophia.inria.fr

Publication date: June 1, 2004

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