On the preservation of instability of mechanical systems under the evolution of dissipative forces

The mechanical systems described by the Lagrange differential equations of the second kind with nonstationary evolution of dissipative forces are studied. It is assumed that the evolution results in domination, or disappearing of dissipative forces. In the case of nonapplicability of known for nonstationary linearizations classical criteria, the theorems on the instability by the linear approximation of the equilibrium position are proved. The systems with essentially nonlinear dissipative forces are investigated. It is assumed that dissipative forces are determined by the homogeneous Rayleigh function, or depend on generalized coordinates. For such systems, the conditions of instability of the equilibrium position are also obtained.