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 |
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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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