Mean-motion resonances in satellite-disc interactions

Mean-motion resonances between a Keplerian disc and an orbiting companion are analysed within a Hamiltonian formulation using complex canonical Poincaré variables, which are ideally suited to the description of eccentricity and inclination dynamics. Irreversibility is introduced by allowing for dissipation within the disc. A method is given for determining the rates of change of eccentricity and inclination variables of the disc and companion associated with resonances of various orders, including both reversible and irreversible effects, which extend and generalize previous results. Preliminary applications to protoplanetary systems and close binary stars are discussed.