On the Stability of the Homographic Polygon Configuration in the Many-Body Problem

Cattani, Carlo and Prokopenya, Alexander N. (2005) On the Stability of the Homographic Polygon Configuration in the Many-Body Problem. Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze FF.MM.NN (LXXXI-LXXXII). ISSN 1825-1242

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Abstract

In this paper the stability of a new class of exact symmetrical solutions in the Newtonian gravitational (n + 1) -body problem is studied. This class of solution follows from a suitable geometric distribution of the (n+1) -bodies, and initial conditions, so that the solution is represented geometrically by an oscillating regular polygon with n sides rotating non-uniformly about its center. The body having a mass m0 is at the center of the polygon, while n bodies having the same mass m are at the vertices of the polygon and move about the central body in identical elliptic orbits. It is proved that for n = 2 and for regular polygons 3 <= n <= 6 each corresponding solution is unstable for any value of the central mass m0 . For n => 7 the solution is linearly stable if both

Item Type:	Article
Subjects:	M.U.S. - Miscellanea > Atti Accademia Peloritana > Classe di Scienze Fisiche, Matematiche e Naturali
Depositing User:	Mr Nunzio Femminò
Date Deposited:	10 Jun 2005
Last Modified:	13 Apr 2010 11:21
URI:	http://cab.unime.it/mus/id/eprint/267

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