Bifurcations in systems with friction: basic models and methods

Examples of irregular behavior of dynamical systems with dry friction are discussed. A classification of frictional contacts with respect to their dimensionality, associativity, and the possibility of interruptions is proposed and basic models showing typical features are stated. In particular, bifurcation conditions for equilibrium families are obtained and formulas for the monodromy matrix for systems with friction are constructed. It is shown that systems with non-associated contacts possess singularities that lead to the nonexistence or nonuniqueness of phase trajectories; these results generalize the paradoxes of Painlev and Jellett. Owing to such behavior, a number of earlier results, including the problem on the motion of a rigid body on a rough plane, require an improvement.