Dynamics of the parabolic restricted three-body problem

•We study planar parabolic restricted three body problem with two equal masses.•We classify the final evolution of a particle after the close approach of the bodies.•The role of some invariant manifolds in the dynamics is shown.•Description of the global flow in terms of the final evolution of the s...

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Veröffentlicht in:Communications in nonlinear science & numerical simulation Jg. 29; H. 1-3; S. 400 - 415
Hauptverfasser: Barrabés, Esther, Cors, Josep M., Ollé, Mercè
Format: Journal Article Verlag
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2015
Schlagworte:
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Classificació AMS
Enginyeria mecànica
Final evolutions
Global dynamics
Invariant manifolds
Matemàtiques i estadística
Orbits
Parabolic restricted three-body problem
Problema dels tres cossos
Three-body problem
Àrees temàtiques de la UPC
Òrbites
Parabolic restricted three-body problem
Final evolutions
Global dynamics
Invariant manifolds
ISSN:1007-5704, 1878-7274
Online-Zugang:Volltext
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Zusammenfassung:•We study planar parabolic restricted three body problem with two equal masses.•We classify the final evolution of a particle after the close approach of the bodies.•The role of some invariant manifolds in the dynamics is shown.•Description of the global flow in terms of the final evolution of the solutions. The main purpose of the paper is the study of the motion of a massless body attracted, under the Newton’s law of gravitation, by two equal masses moving in parabolic orbits all over in the same plane, the planar parabolic restricted three-body problem. We consider the system relative to a rotating and pulsating frame where the equal masses (primaries) remain at rest. The system is gradient-like and has exactly ten hyperbolic equilibrium points lying on the boundary invariant manifolds corresponding to escape of the primaries in past and future time. The global flow of the system is described in terms of the final evolution (forwards and backwards in time) of the solutions. The invariant manifolds of the equilibrium points play a key role in the dynamics. We study the connections, restricted to the invariant boundaries, between the invariant manifolds associated to the equilibrium points. Finally we study numerically the connections in the whole phase space, paying special attention to capture and escape orbits.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2015.05.025