%0 Journal Article
%T A Separating Surface for Sitnikov-like n+1-body Problems
%A Lennard Bakker
%A Skyler Simmons
%J Mathematics
%D 2014
%I arXiv
%X 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
%U http://arxiv.org/abs/1410.2636v3