Chaotic Motion of an Ellipsoidal Satellite. I.

The spin-orbit coupling problem for a satellite influenced by tidal torque is investigated. Melnikov's integrals are evaluated at the saddle point of the equilibrium solution, clearly establishing the nonintegrability of the system. Then, using the asymptotic methods of Krylov, Bogoliubov, and Mitropolsky, semiresonant and resonant cases are discussed analytically. Some interesting features (e.g., strange attractors) have been observed in the numerical computations.