The existence of transversal homoclinic orbits in a planar circular restricted four-body problem

被引：0
|
作者：
Zhikun She
Xuhua Cheng
Cuiping Li
机构：
[1] Beihang University,SKLSDE, LMIB and School of Mathematics and Systems Science
来源：
Celestial Mechanics and Dynamical Astronomy | 2013年 / 115卷
关键词：
Transversal homoclinic orbits; Hamiltonian systems; Melnikov method; Non-canonical transformation; Stable manifold theorem;
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摘要：
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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页码：299 / 309
页数：10
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