Mathematics – Dynamical Systems
Scientific paper
Jun 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..39..191m&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 39, no. 2, 1986, p. 191-198.
Mathematics
Dynamical Systems
3
Dynamical Systems, Gravitational Effects, Poincare Problem, Solar System, Systems Stability, Three Body Problem, Chaos, Kinematics, Particle Collisions, Particle Motion, Particle Trajectories
Scientific paper
The autonomous dynamical system consisting of parallel planes of constant mass density moving under their mutual gravitational attraction is of interest for testing diverse astrophysical models of gravitational relaxation. The simplest nonintegrable system consists of three sheets. In this paper the dynamics and stability of this one-dimensional 'solar system' is systematically investigated. A linear transformation of the coordinates reduces the problem to that of a falling body constrained by oblique boundaries. By constructing a Poincare surface of section, it is found that regions of stability and chaos coexist. This behavior is predicted by the KAM theorem for systems having 'smoother' trajectories in phase space, but does not apply here because of the discontinuity in acceleration experienced by each sheet during an encounter. The results of numerical experiments indicate that chaotic regions may be associated with trajectories which contain nearly triple collisions of the three particles.
Matulich A.
Miller Bruce N.
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