The rhomboidal symmetric four-body problem

Details The rhomboidal symmetric four-body problem The rhomboidal symmetric four-body problem

Apr 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012cemda.tmp...20w&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Online First

Astronomy and Astrophysics

Astronomy

Symmetric Four-Body Problem, Levi-Civita Regularization, Periodic Motion, Resonance, Invariant Tori, Collision Manifold

Scientific paper

We consider the planar symmetric four-body problem with two equal masses m 1 = m 3 > 0 at positions (±x 1(t), 0) and two equal masses m 2 = m 4 > 0 at positions (0, ±x 2(t)) at all times t, referred to as the rhomboidal symmetric four-body problem. Owing to the simplicity of the equations of motion this problem is well suited to study regularization of the binary collisions, periodic solutions, chaotic motion, as well as the four-body collision and escape manifolds. Furthermore, resonance phenomena between the two interacting rectilinear binaries play an important role.

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