The stability of equilibrium in systems with friction

Mechanical systems with non-ideal geometrical constraints are considered. The possible lack of uniqueness of the solution of the problem of determining the generalized accelerations and reactions with respect to specified coordinates and velocities is taken into account in solving the problem of the stability of an equilibrium state. A number of necessary and sufficient conditions of stability are obtained. It is shown that the results are also applicable in the case of unilateral constraints subject to the condition that a specific hypothesis concerning the character of the impacts on the constraints is adopted. A problem on the stability of a rigid body on a rough plane in the two-dimensional case is solved as an example.