Numerical analysis of a class of planar three-body systems with nonzero angular momenta

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Celestial Mechanics: Three-Body Problem, Dynamical Evolution

Scientific paper

A class of the planar three-body systems with nonzero angular momenta is studied. The main aim is to find out the effects of this system's initial configuration on its dynamical evolution. According to the homology map first suggested by Agekian & Anosova, a planar three-body system corresponds to a point of one of 4 characteristic regions. By comparing the evolutions of the homology drops in the nonzero-angular-momentum three-body systems with the zero-angular-momentum systems (P.Heinamaki et al, 1999), we found the similarity of the mixing extent of the homology drops in the homology map, and the difference in the functions of the number of surviving systems versus time in those drops. And through the statistics of the evolution time of the systems, we obtain the following results: (i) the mean lifetimes of the systems of the 4 regions are different; (ii) there is an exponential relationship between the number N of the surviving systems and the evolution time t.

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