Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1283..128a&link_type=abstract
MATHEMATICS AND ASTRONOMY: A JOINT LONG JOURNEY: Proceedings of the International Conference. AIP Conference Proceedings, Volum
Astronomy and Astrophysics
Astronomy
Celestial Mechanics, Saturn, Differential Equations, Celestial Mechanics, Saturn, Ordinary And Partial Differential Equations, Boundary Value Problems
Scientific paper
The planar n+1 ring body problem consists of n bodies of equal mass m uniformly distributed around a central body of mass m0. The bodies are rotating on its own plane about its center of mass with a constant angular velocity. Since Maxwell introduced the problem to understand the stability of Saturn's rings, many authors have studied and extended the problem. In particular, we proved that if forces that are functions of the mutual distances are considered the n-gon is a central configuration. Examples of this kind are the quasi-homogeneous potentials.
In a previous work we analyzed the linear stability of a system where the potential of the central body is a Manev's type potential. By introducing a perturbation parameter (ɛ0) to the Newtonian potential associated with the central primary, we showed that unstable cases for the unperturbed problem, for n<=6, may become stable for some values of the perturbation.
The purpose of this paper is to show that it is possible to increase the range of values of the mass parameter (μ = m/m0) and the parameter (V0) in order to render a stable configuration. In order to get it, we introduce a second perturbation term (with parameter (V1) to the Newtonian potential of the bodies in the ring. We show some results for the problem with n = 7.
Arribas María
Elipe Antonio
Palacios Manuel
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