Relaxation oscillations in tidally evolving satellites (Q1383208)

The authors study the problem of rotational evolution of an axisymmetric natural satellite in an orbit inclined with respect to an invariant plane under the influence of tidal torques. It is shown that the equations of motion, averaged with respect to the spin and orbit variables, possess a limit cycle that corresponds to an alternation between states of synchronous spin at low obliquity and subsynchronous spin at high obliquities of near \(90^\circ\). Conditions for the existence of this limit cycle are found. It is shown numerically that triaxial satellites may also exhibit such limit cycle dynamics, but only at very high inclinations and for large values of tidal dissipation.