Celletti A., Chierchia L.
Construction of stable periodic orbits for the spin-orbit
problem of celestial mechanics
(55K, Plain TEX)
ABSTRACT. Birkhoff periodic orbits associated to spin--orbit resonances in Celestial
Mechanics and in particular to the Moon--Earth and Mercury--Sun systems
are considered. A general method (based on a quantitative version of the
Implicit Function Theorem) for the construction of such orbits with
particular attention to ``effective estimates"
on the size of the perturbative parameters is presented and tested
on the above mentioned systems. Lyapunov stability of the periodic
orbits (for small values of the perturbative parameters) is proved by
constructing KAM librational invariant surfaces trapping the periodic orbits.