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Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem · arXivDesk

1105.5618May 27, 201113 pages, 1 figure

Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

Lennard F. Bakker, Scott C. Mancuso, Skyler C. Simmons

Classical Analysis and ODEs

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Abstract

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 $m\in(0,1]$

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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∈(0,1] as the parameter. This reduces the linear stability analysis to the computation of two eigenvalues of a 3× 3 matrix for each m∈(0,1] obtained from numerical integration of the linearized regularized equations along only the first one-eighth of each regularized periodic orbit.

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The paper addresses: Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem.
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∈(0,1] as the parameter.