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

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

arxiv: 0905.4519 · v1 · pith:DCGCMKZ5new · submitted 2009-05-27 · 🧮 math.DS

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 This is my paper

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keywords problemlinearstabilitysymmetricbinarycollinearcollisionfour-body

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

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