Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem |
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Authors: | Lennard F Bakker Tiancheng Ouyang Duokui Yan Skyler Simmons |
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Institution: | (1) School of Mathematics and Statistics, Napier University, 219, Colinton Road, Edinburgh, EH14 1DJ, Scotland |
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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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