Spacecraft observations of Saturn's rings show evidence of an activeaggregation-disaggregation process triggered by periodic influences from thenearby moons. This leads to clumping and break-up of the ring particles attime-scales of the order of a few hours. A mathematical model has beendeveloped to explain these dynamics in the Saturn's F-ring and B-ring [3], theimplications of which are in close agreement with the empirical results. Inthis paper, we conduct a rigorous analysis of the proposed forced dynamicalsystem for a class of continuous, periodic and zero-mean forcing functions thatmodel the ring perturbations caused by the moon flybys. In specific, we derivethe existence of at least one periodic solution to the dynamic system with theperiod equal to the forcing period of the moon. Further, conditions for theuniqueness and stability of the solution and bounds for the amplitudes of theperiodic solution are derived.
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