%0 Journal Article
%T Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
%A Lennard F. Bakker
%A Scott C. Mancuso
%A Skyler C. Simmons
%J Mathematics
%D 2011
%I arXiv
%R 10.1007/s10569-012-9402-6
%X We apply the symmetry reduction method of Roberts to numerically analyze the linear stability of a one-parameter family of symmetric periodic orbits with regularizable simultaneous binary collisions in the planar pairwise symmetric four-body problem with a mass $m\in(0,1]$ as the parameter. This reduces the linear stability analysis to the computation of two eigenvalues of a $3\times 3$ matrix for each $m\in(0,1]$ obtained from numerical integration of the linearized regularized equations along only the first one-eighth of each regularized periodic orbit. The results are that the family of symmetric periodic orbits with regularizable simultaneous binary collisions changes its linear stability type several times as $m$ varies over $(0,1]$, with linear instability for $m$ close or equal to 0.01, and linear stability for $m$ close or equal to 1.
%U http://arxiv.org/abs/1105.5618v2