Investigation of partial asymptotic stability and instability based on the limiting equations (Q1108091)

A new type of limiting equations is studied, used to investigate the asymptotic stability and instability of unperturbed motion with respect to some of the variables, based on the Lyapunov function with a singleconstant derivative, without assuming that the perturbed motions are bounded over the non-controlled coordinates. Sufficient conditions are derived for the asymptotic stability with respect to the generalized velocities and some of the generalized coordinates of the zero position of equilibrium of the non-autonomous, holonomic and non-holonomic mechanical systems under the action of dissipative forces.