Displacement Potentials in Non-Smooth Dynamics

Overview & Synopsis

The paper treats the evaluation of the accelerations in rigid multibody systems which are subjected to displacement dependent set-valued force interactions. The interaction laws are represented by non-smooth 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.