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Title: Study and simulation of the planar and circular restricted three-body problem
Author: Solà Vilalta, Albert
Director: Benseny, Antoni
Keywords: Problema dels tres cossos
Problema dels dos cossos
Anàlisi numèrica
Lleis de Kepler
Caos (Teoria de sistemes)
Varietats (Matemàtica)
Sistemes dinàmics diferenciables
Three-body problem
Two-body problem
Numerical analysis
Kepler's laws
Chaotic behavior in systems
Manifolds (Mathematics)
Differentiable dynamical systems
Issue Date: 24-Jul-2015
Abstract: We study the Planar and Circular Restricted Three-Body Problem, as an idealization of the Three-Body Problem. We follow a dynamical systems approach. Once the main characteristics of the problem have been described, we try to explore a little bit the chaos of the system. Without pretending to be systematic, we focus on final evolutions. In particular, the parabolic final evolutions are used to show evidence of chaos, as they correspond to the invariant manifolds of the periodic orbit at infinity, which intersect non-tangentially in a certain Poincaré section, giving rise to transversal homoclinic points of the associated Poincaré map. Furthermore, we try to outline some differences between the integrable Kepler Problem and the non-integrable Planar and Circular Restricted Three-Body Problem, which can be explained by the splitting of the two previously mentioned invariant manifolds. The use of numerical methods has been fundamental for the realization of this work.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Antoni Benseny Ardiaca
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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