The stiffness of quasilinear gyroscopically coupled systems with respect to low and high frequency periodic perturbations

The stability of the equilibrium of gyroscopically coupled quasilinear systems with many degrees of freedom is investigated when there is dissipation and a periodic perturbation which is not necessarily of small amplitude. Non-potential forces (customarily referred to as radial correction forces or circulating forces) act together with potential forces. Under conditions of a low- and high-frequency periodic perturbation, classes of systems are distinguished using Lyapunov functions which possess the property of unperturbability, that is, their qualitative structure remains almost the same as in the case of autonomous systems. Generalizations to the case of non-periodic perturbations are possible.