Normal Forms for Perturbed Keplerian Systems

Perturbations of rotating and nonrotating Keplerian systems with two and three degrees of freedom are considered. The dominant (unperturbed) part of the Hamilton function is the sum of the two-body part and the Coriolis term. The flows associated to these two components are used to put the whole system into normal form by means of symplectic transformations. Three different situations are analysed: (i) the two-body effect dominates the Coriolis part (slow rotations), (ii) the Coriolis effect is stronger than the two-body Hamiltonian (very fast rotations), and (iii) the two effects are comparable (moderate rotations). After performing the transformations to normal form, the system is reduced by one or two degrees of freedom. We describe the reduced phase spaces by calculating the invariants of the symmetry groups associated to the different normal forms (reduced systems). The technique is applied to the reduction of a Hamiltonian system modelling the trapping mechanisms for the electron of a strongly ionized hydrogen atom.