Parametric Stability in Robe's Problem

In this work we have given a Hamiltonian formulation to Robe's problem, obtaining again the classic results. We have computed the resonances existing in the circular case and obtained some information with regard to the linear stability of the central equilibrium of Robe's problem in the elliptic case. In some critical cases we have constructed, in the parameter plane, the boundary curves that separate the regions of stability and instability.