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Celestial Mechanics and Dynamical Astronomy

, Volume 110, Issue 3, pp 271–290 | Cite as

Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem

  • Lennard F. Bakker
  • Tiancheng Ouyang
  • Duokui Yan
  • Skyler Simmons
Original Article

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.

Keywords

N-body problem Regularization Periodic orbits Stability Simultaneous binary collision 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Lennard F. Bakker
    • 1
  • Tiancheng Ouyang
    • 1
  • Duokui Yan
    • 2
  • Skyler Simmons
    • 1
  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA
  2. 2.Chern Institute of MathematicsNankai UniversityTianjinPeople’s Republic of China

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