Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem |
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Authors: | Lennard F Bakker Tiancheng Ouyang Duokui Yan Skyler Simmons Gareth E Roberts |
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Institution: | (2) Mathematics Institute, University of Warwick, Warwick, UK; |
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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. In both problems, the assumed symmetries reduce the determination of linear stability
to the numerical computation of a single real number. For the collinear problem, this verifies the earlier numerical results
of Sweatman for linear stability with respect to collinear and symmetric perturbations. |
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Keywords: | |
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