Tame and chaotic behavior in the planar isosceles 3body problem
Abstract
It is shown that every planar isosceles solution of the threebody problem encounters a collision of the symmetric particles, either forward or backward in time. Regularizing analytically this collision, the solution has at least a Syzygy configuration and/or leads to a total collapse. Further simple results support the intuitive image on the tame local behavior of the motion as long as it does not lead to a triple collision. As a main result, it is proved that total collapse singularities can be regularized in a C1 fashion with respect to time, for all values of the masses. Using symbolic dynamics, the chaotic character of the C1regularized solutions is pointed out.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 1991
 Bibcode:
 1991CeMDA..50..313D
 Keywords:

 Chaos;
 Many Body Problem;
 Orbital Mechanics;
 Three Body Problem;
 Gravitational Collapse;
 Spatial Distribution;
 Two Dimensional Models;
 Physics (General)