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Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem · arXivDesk

0905.4519May 27, 200916 pages, 4 figures

Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem

Lennard F. Bakker, Tiancheng Ouyang, Skyler Simmons, Duokui Yan, Gareth E. Roberts

Abstract

We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

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The paper addresses: Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem.
We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses.