Formulation of rigid body systems with nonsmooth and multivalued interactions

Abstract

This paper treats the formulation of interaction laws in rigid multibody systems. The interaction laws may be represented by a certain class of convex C potential functions and then derived through subdifferentiation. 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 or damper combinations. Impacts are excluded. A generalization of the principles of d’Alembert, Jourdain, and Gauss in terms of variational inequalities will be given. The paper is organized as follows. In Section 2 some preliminaries about directional derivatives and subdifferentials are stated, cp. [1]. Section 3 contains the formulation of the differential inclusions of rigid multibody systems as well as the Principle of d’Alembert. From that, and using the results of Section 2, the Principles of Jourdain and Gauss are derived in Sections 4 and 5. Finally, Section 6 contains the Principle of Least Constraints, i.e. a minimization problem in terms of the unknown accelerations.