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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. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

preprint2009arXivOpen access
Lennard F. BakkerTiancheng OuyangSkyler SimmonsDuokui YanGareth E. Roberts
math.DS
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Open access5 authors1 topic
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Lennard F. BakkerTiancheng OuyangSkyler SimmonsDuokui YanGareth E. Roberts

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