The principles of d'Alembert, Jourdain, and Gauss in nonsmooth dynamics - Part I: Scleronomic multibody systems

The paper treats the evaluation of the accelerations in rigid multibody systems which are subjected to set-valued force interactions. The interaction laws may be represented by non-smooth potential functions, and then 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, dry friction, or prestressed springs with play. Impacts are excluded. A generalization of the classical principles of d'Alembert, Jourdain, and Gauss in terms of variational inequalities will be given. A strictly convex minimization problem depending on the unknown accelerations of the system will be stated: known in classical mechanics as the Principle of least Constraints.