A Separating Surface for Sitnikov-like n+1-body Problems
Dynamical Systems
2014-11-13 v3
Abstract
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless particle on the z-axis. The study of the motion of this particle can then be modelled as a time-dependent Hamiltonian System. We give a geometric construction of a surface in the three-dimensional phase space separating orbits for which the massless particle escapes to infinity from those for which it does not. The construction is demonstrated numerically in a few examples
Cite
@article{arxiv.1410.2636,
title = {A Separating Surface for Sitnikov-like n+1-body Problems},
author = {Lennard Bakker and Skyler Simmons},
journal= {arXiv preprint arXiv:1410.2636},
year = {2014}
}
Comments
24 pages, 15 figures