ON PERTURBED 2-BODY PROBLEMS AND HARMONIC-OSCILLATORS

The possibility of achieving linearization (i.e. reduction of the equa tions of motion to second-order differential equations corresponding t o harmonic oscillators) of a class of r(-n)-perturbed Kepler problems is investigated by using BF focal-type canonical variables. We show th at the only r(-n)-perturbation of the considered class which admits ex act linearization is that corresponding to the Deprit-type potentials (say, for n = 2) constructed within the framework of Artificial Satell ite Theory. Approximate linearization is also obtained for perturbatio ns involving other powers of the radial distance. In any case, this pr ocess requires the use of a fictitious time of the true anomaly type.