On the restrited three-body problem when the mass parameter is small

DOI10.1007/BF01230662zbMath0505.70012MaRDI QIDQ4742339

Jaume Llibre

Publication date: 1982

Published in: Celestial Mechanics (Search for Journal in Brave)

zbMATH Keywords

restricted three-body problemcollisionsymmetric periodic orbitsparabolic orbitsglobal flow of two-body rotating problemmass parameter small

Mathematics Subject Classification ID

Three-body problems (70F07) Celestial mechanics (70F15)

Related Items (17)

The global phase space for the 2- and 3-dimensional Kepler problems ⋮ Transversal ejection-collision orbits for the restricted problem and the Hill's problem with applications ⋮ On the elliptic restricted three-body problem ⋮ Regularization of the Hill four-body problem with oblate bodies ⋮ Computer assisted proofs for transverse collision and near collision orbits in the restricted three body problem ⋮ To and fro motion for the hydrogen atom in a circularly polarized microwave field ⋮ Ejection-collision orbits in the RTBP ⋮ Regularisation in Ejection-Collision Orbits of the RTBP ⋮ Analytical and numerical results on families of \(n\)-ejection-collision orbits in the RTBP ⋮ Transit regions and ejection/collision orbits in the RTBP ⋮ Periodic orbits for the perturbed planar circular restricted 3-body problem ⋮ Transversal ejection-collision orbits in Hill's problem forC?1 ⋮ A note on the elliptic restricted three-body problem ⋮ A search for triple collision orbits inside the domain of the free-fall three-body problem ⋮ Numerical experiments of the planar equal-mass three-body problem: The effects of rotation ⋮ Generalized analytical results on \(n\)-ejection-collision orbits in the RTBP. Analysis of bifurcations ⋮ Ejection and collision orbits of the spatial restricted three-body problem

Cites Work

• Oscillatory solutions in the planar restricted three-body problem
• A stable manifold theorem for degenerate fixed points with applications to celestial mechanics
• [https://portal.mardi4nfdi.de/wiki/Publication:3945645 A note on a conjecture of Poincar�]
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
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