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Celestial Mechanics and Dynamical Astronomy

, Volume 109, Issue 3, pp 229–239 | Cite as

Periodic solutions with alternating singularities in the collinear four-body problem

  • Tiancheng Ouyang
  • Duokui Yan
Original Article

Abstract

This paper gives an analytic proof of the existence of Schubart-like orbit, a periodic orbit with singularities in the symmetric collinear four-body problem. In each period of the Schubart-like orbit, there is a binary collision (BC) between the inner two bodies and a simultaneous binary collision (SBC) of the two clusters on both sides of the origin. The system is regularized and the existence is proved by using a “turning point” technique and a continuity argument on differential equations of the regularized Hamiltonian.

Keywords

Celestial mechanics Four-body problem Binary collision Simultaneous binary collision Periodic solution with singularity 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of MathematicsBrigham Young UniversityProvoUSA
  2. 2.Chern Institute of Mathematics, Nankai UniversityTianjinPeople’s Republic of China

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