A Hopf variables view on the libration points dynamics

Abstract

The dynamics about the libration points of the Hill problem is investigated analytically. In particular, the use of Lissajous variables and perturbation theory allows to reduce the problem to a one degree of freedom Hamiltonian depending on two physical parameters. The invariant manifolds structure of the Hill problem is then disclosed, yet accurate computations are limited to energy values close to that of the libration points.

References in corpus (1)

• Bifurcation sequences in the symmetric 1:1 Hamiltonian resonance

Cited by in corpus (5)

• Higher Order Approximation to the Hill Problem Dynamics about the Libration Points
• Structure of the center manifold of the L1 and L2 collinear libration points in the restricted three-body problem
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• A torsion-based solution to the hyperbolic regime of the J2-problem