Displacement Potentials in Non-Smooth Dynamics

The paper treats the evaluation of the accelerations in rigid multibody systems which are subjected to displacement dependent setvalued force interactions. The interaction laws are represented by nonsmooth displacement potentials and derived through generalized differentiation. The resulting multifunctions contain the cases of smooth force characteristics, bilateral constraints, as well as combinations of them like unilateral constraints or prestressed springs with play. Impacts are excluded. A generalization of the classical principles of d ' Alembert, Jourdain, and Gauss in terms of hemi-variational inequalities is given. A strictly convex minimization problem depending on the unknown accelerations is stated, known in classical mechanics as the Principle of Least Constraints. The theory is applied to unilaterally constrained systems.