Invariant manifolds of L_3 and horseshoe motion in the restricted three-body problem
In this paper, we consider horseshoe motion in the planar restricted three-body problem. On one hand, we deal with the families of horseshoe periodic orbits (which surround three equilibrium points called L3, L4 and L5), when the mass parameter µ is positive and small; we describe the structure of s...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2005 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1227 |
| Acceso en línea: | https://hdl.handle.net/2117/1227 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations Differentiable dynamical systems Dynamics periodic orbits invariant stable and unstable manifolds homoclinic orbits restricted problem Equacions diferencials ordinàries Sistemes dinàmics diferenciables Teoria ergòdica Partícules (Física nuclear) Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics |
| Sumario: | In this paper, we consider horseshoe motion in the planar restricted three-body problem. On one hand, we deal with the families of horseshoe periodic orbits (which surround three equilibrium points called L3, L4 and L5), when the mass parameter µ is positive and small; we describe the structure of such families from the two-body problem (µ = 0). On the other hand, the region of existence of horseshoe periodic orbits for any value of µ ∈ (0, 1/2] implies the understanding of the behaviour of the invariant manifolds of L3. So, a systematic analysis of such manifolds is carried out. As well the implications on the number of homoclinic connections to L3, and on the simple infinite and double infinite period homoclinic phenomena are also analysed. Finally, the relationship between the horseshoe homoclinic orbits and the horseshoe periodic orbits are considered in detail. |
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