The rhomboidal symmetric four-body problem |
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| Authors: | J?rg Waldvogel |
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| Institution: | 1. Seminar for Applied Mathematics, Swiss Federal Institute of Technology ETH, 8092, Zurich, Switzerland
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| Abstract: | 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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