On the establishment and evolution of orbit-orbit resonances

A theory which suggests that in the case of planetary satellites, a tidally induced torque acting on the satellites may play an essential role on the evolution of the observed resonances is investigated as it applies to the three resonances among pairs of satellites of Saturn. Three stages are investigated: a theoretical description of transition is developed for a simple time dependent pendulum plus constant applied torque; the two body gravitational interaction is expanded and reduced to a one dimensional time independent Hamiltonion; and the model is applied to Saturn resonances. Although the theory proves successful in the Saturn case, it is less successful in the Tital-Hyperion case in providing a resonable time scale for the damping of the amplitude of liberation.