Evolution and stability of the theoretically predicted families of periodic orbits in the N-body ring problem

Details Evolution and stability of the theoretically predicted families of periodic orbits in the N-body ring problem Evolution and stability of the theoretically predicted families of periodic orbits in the N-body ring problem

Mar 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005a%26a...432..713p&link_type=abstract

Astronomy and Astrophysics, Volume 432, Issue 2, March III 2005, pp.713-729

Astronomy and Astrophysics

Astrophysics

9

Celestial Mechanics, Chaos

Scientific paper

We theoretically investigate the existence of families of periodic orbits in the planar N-body ring problem and we give a qualitative picture of the motion of a small particle. This study yields four families of periodic orbits which we also found numerically: two families of periodic orbits around the central body and two families around all the peripherals. These results are valid for different values of N and β. Also we investigate the evolution of simple periodic motions as well as their stability. We found stable and unstable orbits around the central body, around all the peripherals and around one or more peripherals which form rings of stability. Some families present other types of bifurcations, such as bifurcations of families of non-symmetric periodic orbits of the same period and period-doubling bifurcations.

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