The invariant manifold structure of the spatial Hill's problem

DOI10.1080/14689360412331313039zbMath1062.70026OpenAlexW2071271549MaRDI QIDQ4651112

M. Marcote, Gerard Gomez, Josep Maria Mondelo González

Publication date: 21 February 2005

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689360412331313039

zbMATH Keywords

center manifoldstwo libration points

Mathematics Subject Classification ID

Celestial mechanics (70F15) Dynamical systems in classical and celestial mechanics (37N05) Homoclinic and heteroclinic trajectories for nonlinear problems in mechanics (70K44)

Related Items (15)

Numerical determination of homoclinic and heteroclinic orbits at collinear equilibria in the restricted three-body problem with oblateness ⋮ Constructing invariant tori for the spatial Hill lunar problem ⋮ A Framework for Constructing Transfers Linking Periodic Libration Point Orbits in the Spatial Circular Restricted Three-Body Problem ⋮ Examples of integrable and non-integrable systems on singular symplectic manifolds ⋮ Numerical study of the geometry of the phase space of the Augmented Hill Three-Body problem ⋮ A Hopf variables view on the libration points dynamics ⋮ Hill's approximation in a restricted four-body problem ⋮ Fully numerical computation of heteroclinic connection families in the spatial three-body problem ⋮ Semianalytical Computation of Heteroclinic Connections Between Center Manifolds with the Parameterization Method ⋮ Determination of the doubly symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem ⋮ Dynamics Associated with the Normally Hyperbolic Invariant Manifold that Governs the Ionization of Hydrogen in a Circularly Polarized Electric Field ⋮ Higher order approximation to the Hill problem dynamics about the libration points ⋮ Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP ⋮ Mission design through averaging of perturbed Keplerian systems: the paradigm of an Enceladus orbiter ⋮ On the stability of satellites at unstable libration points of Sun-planet-Moon systems

Uses Software

• LAPACK

Cites Work

• Study of the transfer from the Earth to a halo orbit around the equilibrium point \(L_ 1\)
• New families of periodic orbits in Hill's problem of three bodies
• Central stable/unstable manifolds and the destruction of KAM tori in the planar Hill problem
• On the vertical families of two-dimensional tori near the triangular points of the bicircular problem
• Non-continuation of integrals of the rotating two-body problem in Hill's lunar problem
• Dynamics in the center manifold of the collinear points of the restricted three-body problem
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
• Connecting orbits and invariant manifolds in the spatial restricted three-body problem
• Low Energy Transit Orbits in the Restricted Three-Body Problems
• The dynamics around the collinear equilibrium points of the RTBP
• Non-integrability of Hill's lunar problem.

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