Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002cemda..82..179s&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 82, Issue 2, p. 179-201 (2002).
Astronomy and Astrophysics
Astronomy
12
Four-Body Problem, Collinear Motion, Periodic Orbits, Binary Scattering, Four-Body Problem, Collinear Motion, Periodic Orbits, Binary Scattering
Scientific paper
Numerical simulations of the one-dimensional Newtonian four-body problem have been conducted for the special case in which the bodies are distributed symmetrically about the centre of mass. Simulations show a great similarity between this problem and the one-dimensional Newtonian three-body problem. As in that problem the orbits can be divided into three different categories which form well-defined regions on a Poincaré section: there is a region of quasiperiodic orbits about a Schubart-like periodic orbit, there is a region of fast-scattering encounters and in between these two regions there is a chaotic scattering region. The Schubart-like periodic orbit's stability to perturbation is studied. It is apparently stable in one-dimension but is unstable in three-dimensions.
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