4 research outputs found
Chaos in the one-dimensional gravitational three-body problem
We have investigated the appearance of chaos in the 1-dimensional Newtonian
gravitational three-body system (three masses on a line with pairwise
potential). We have concentrated in particular on how the behavior changes when
the relative masses of the three bodies change (with negative total energy).
For two mass choices we have calculated 18000 full orbits (with initial states
on a lattice on the Poincar\'e section) and obtained dwell time
distributions. For 105 mass choices we have calculated Poincar\'e maps for
starting points. Our results show that the Poincar\'e section
(and hence the phase space) divides into three well defined regions with orbits
of different characteristics: 1) There is a region of fast scattering, with a
minimum of pairwise collisions and smooth dependence on initial values. 2) In
the chaotic scattering region the interaction times are longer, and both the
interaction time and the final state depend sensitively on the starting point
on the Poincar\'e section. For both 1) and 2) the initial and final states
consists of a binary + single particle. 3) The third region consists of
quasiperiodic orbits where the three masses are bound together forever. At the
center of the quasiperiodic region there is the periodic Schubart orbit, whose
stability turns out to correlate strongly with the global behavior.Comment: 24 pages of text (REVTEX 3.0) + 21 pages of figures. Figures are only
available in paper form, ask for a preprint from the author