Abstract
We analytically prove the existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. This is an extension of our previous proof of the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar fully symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for m between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when 0.54 ≤ m ≤ 1, and are linearly unstable when 0 < m ≤ 0.53.
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An erratum to this article can be found at http://dx.doi.org/10.1007/s10569-012-9402-6.
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Bakker, L.F., Ouyang, T., Yan, D. et al. Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem. Celest Mech Dyn Astr 110, 271–290 (2011). https://doi.org/10.1007/s10569-011-9358-y
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DOI: https://doi.org/10.1007/s10569-011-9358-y