The dynamical evolution of the planetary rings is simulated by means of a numerical model in which particles interact through mutual attraction and inelastic collisions. We use a mixed simulation: a deterministic integration of the N - body problem for large distances (“particle-mesh” method with an expansion of density and potential in spherical harmonics) and a Monte Carlo treatment for the close encounters. The implementation is done in the Connection Machine in order to be able to make a detailed simulation using a greater number of particles (of the order of 105). The deterministic calculation of the action of a shepherding satellite on the particles will allow us to study the effect of resonances on the formation and the evolution of the sharp edges of the rings.
