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This article is cited in 13 scientific papers (total in 13 papers)
Invariant Manifolds at Infinity of the RTBP and the Boundaries of Bounded Motion
Regina Martíneza, Carles Simób a Departament de Matemàtiques, Universitat Autònoma de Barcelona,
Edifici C, 08193 Bellaterra, Barcelona, Spain
b Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona,
Gran Via 585, 08007, Barcelona, Catalunya, Spain
Abstract:
Invariant manifolds of a periodic orbit at infinity in the planar circular RTBP are studied. To this end we consider the intersection of the manifolds with the passage through the barycentric pericenter. The intersections of the stable and unstable manifolds have a common even part, which can be seen as a displaced version of the two-body problem, and an odd part which gives rise to a splitting. The theoretical formulas obtained for a Jacobi constant C large enough are compared to direct numerical computations showing improved agreement when C increases. A return map to the pericenter passage is derived, and using an approximation by standard-like maps, one can make a prediction of the location of the boundaries of bounded motion. This result is compared to numerical estimates, again improving for increasing C. Several anomalous phenomena are described.
Keywords:
invariant rotational curves, separatrix maps, splitting function, restricted three-body problem.
Received: 20.10.2014 Accepted: 06.11.2014
Citation:
Regina Martínez, Carles Simó, “Invariant Manifolds at Infinity of the RTBP and the Boundaries of Bounded Motion”, Regul. Chaotic Dyn., 19:6 (2014), 745–765
Linking options:
https://www.mathnet.ru/eng/rcd196 https://www.mathnet.ru/eng/rcd/v19/i6/p745
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Abstract page: | 259 | References: | 38 |
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