Numerical determination of homoclinic and heteroclinic orbits at collinear equilibria in the restricted three-body problem with oblateness

DOI10.1007/s10569-005-4441-xzbMath1125.70004OpenAlexW2046456262MaRDI QIDQ819166

Vassilis S. Kalantonis, Christos N. Douskos, E. A. Perdios

Publication date: 22 March 2006

Published in: Celestial Mechanics and Dynamical Astronomy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10569-005-4441-x

zbMATH Keywords

heteroclinic orbitshomoclinic orbitsrestricted three-body problemoblatenessdoubly asymptotic periodic orbits

Mathematics Subject Classification ID

Three-body problems (70F07) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44)

Related Items

Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem ⋮ On the Stability of the Triangular Equilibrium Points in the Elliptic Restricted Three-Body Problem with Radiation and Oblateness ⋮ Poynting-Robertson and oblateness effects on the equilibrium points of the perturbed R3BP: application on Cen X-4 binary system ⋮ Periodic solutions around the collinear equilibrium points in the perturbed restricted three-body problem with triaxial and radiating primaries for binary HD 191408, Kruger 60 and HD 155876 systems

Cites Work

• Symmetric doubly-asymptotic periodic orbits at collinear equilibria
• Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near \(L_ 2\) in the restricted three-body problem
• Non-symmetric doubly-asymptotic orbits at the outer collinear equilibrium point \(L_ 3\)
• Asymptotic orbits and terminations of families in the Copenhagen problem. II
• Asymptotic orbits and terminations of families in the Copenhagen problem
• Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem
• Symmetric doubly asymptotic orbits in the photogravitational restricted three-body problem.
• Collinear equilibria and their characteristic exponents in the restricted three-body problem when the primaries are oblate spheroids
• Stationary solutions and their characteristic exponents in the restricted three-body problem when the more massive primary is an oblate spheroid
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
• The invariant manifold structure of the spatial Hill's problem
• The dynamics around the collinear equilibrium points of the RTBP