Cattani, Carlo and Prokopenya, Alexander N. (2005) On the Stability of the Homographic Polygon Configuration in the ManyBody Problem. Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze FF.MM.NN (LXXXILXXXII). ISSN 18251242

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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 nonuniformly 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 FemminÃ² 
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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