Unilaterality and dry friction: A geometric formulation for two-dimensional rigid body dynamics

The dynamics of a rigid body simply supported on a moving rigid ground in the presence of dry friction is investigated. Rigid body kinematics, in terms of generalized coordinates, and features of contact are discussed. According to the contact laws, a variational formulation is adopted to describe the dynamics and to analyze, in the case of contact, the connection between dynamically possible motions and actual evolution of the system. A geometric method is then proposed which allows the dynamic evolution to be determined without any direct evaluation of the contact forces. Though different situations are possible, depending on the instantaneous values of relative position, velocity and active forces, a unique solution is identified. Examples illustrating applications of the theory are presented.