The invariant manifold structure of the spatial Hill's problem

Abstract

The paper studies the invariant manifolds of the spatial Hill's problem associated to the two liberation points. A combination of analytical and numerical tools allow the normalization of the Hamiltonian and the computation of periodic and quasi-periodic (invariant tori) orbits. With these tools, it is possible to give a complete description of the center manifolds, association to the liberation points, for a large set of energy values.

A systematic exploration of the homoclinic and heteroclinic connections between the center manifolds of the liberation points is also given.

Acknowledgements

This work has been partially supported by grant CIRIT 2001 SGR-70 (Catalonia) and grant BFM2003-09504-C02-01 (MCYT, Spain). M.M. acknowledges the support of the doctoral research grant AP2001-3064 (MECD, Spain).

Notes

if we are to the L₁ liberation point, ω₁ and ω₂ will be close to the horizontal and vertical frequencies, ω and ν, associated to the behaviour around L ₁ given in (7).