On the stability of solutions of dynamical systems with dissipation

Many authors analyzed plane-parallel and spatial motions of realistic rigid bodies in various media. Numerous nonlinear models of the interaction of media and rigid bodies were constructed. For plane-parallel and spatial models, sufficient conditions for the stability of the rectilinear translational motion were found. We prove that under some conditions, such systems may also possess self-oscillating regimes, both stable or unstable. We discuss a natural generalization of force fields in various dissipative dynamical systems with one and two degrees of freedom.