Capture and escape from resonance in the dynamics of the rigid body in viscous medium

Summary The problem of capture and escape from resonance generally arises when certain nonlinear integrable Hamiltonian systems are subjected to non-Hamiltonian perturbation. The essential features of this problem are independent of the nature of the system under consideration. As an example we examine in detail the abovementioned resonance phenomena in rotational motions of a rigid body in a viscous medium. Our analysis is based on the averaging method. Conditions for the existence of the motions captured into resonance are derived. Scattering of the phase trajectories is estimated in the case of passage through resonance without capture.