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

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

Mar 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cemda.109..229o&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 109, Issue 3, pp.229-239

Astronomy and Astrophysics

Astronomy

2

Celestial Mechanics, Four-Body Problem, Binary Collision, Simultaneous Binary Collision, Periodic Solution With Singularity

Scientific paper

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.

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