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

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

2009-05-27

arxiv.org/abs/0905.4519v1

Mathematics

Dynamical Systems

16 pages, 4 figures

Scientific paper

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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