The existence of transversal homoclinic orbits in a planar circular restricted four-body problem |
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| Authors: | Zhikun She Xuhua Cheng Cuiping Li |
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| Institution: | 1. SKLSDE, LMIB and School of Mathematics and Systems Science, Beihang University, 100191, Beijing, China
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| Abstract: | In this paper, we study the existence of transversal homoclinic orbits in a planar circular restricted four-body problem, based on the perturbation theory of integrable Hamiltonian systems. We start from a planar circular restricted four-body model and regard it as a perturbation of the two-body model. Then, in order to conveniently study unbounded orbits, we transform the infinite points to finite points by a non-canonical transformation, arriving at a non-Hamiltonian system with degenerate fixed points. According to the extended Melnikov method, we finally prove that there exist transversal homoclinic orbits in this four-body model. |
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