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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Bakker, L.F., Ouyang, T., Yan, D. et al. Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem. Celest Mech Dyn Astr 108, 147–164 (2010). https://doi.org/10.1007/s10569-010-9298-y
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DOI: https://doi.org/10.1007/s10569-010-9298-y