Periodic solutions with alternating singularities in the collinear four-body problem
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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.
KeywordsCelestial mechanics Four-body problem Binary collision Simultaneous binary collision Periodic solution with singularity
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- Ouyang, T., Yan, D.: Simultaneous Binary Collision for the collinear four body problem (preprint, 2009)Google Scholar