Non-Smooth Mechanics

Abstract

This chapter deals with the non-smoothmodeling ofmechanical systems. In Sect. 3.1 it is reviewed how a mechanical system subjected to bilateral constraints can be formulated as a differential algebraic equation (DAE). The theory is extended in Sect. 3.2 to non-impulsive non-smooth motion, and it is discussed how unilateral contacts, friction and other non-smooth interactions can be modeled by set-valued force laws. In Sect. 3.3 impacts and other impulsive interactions are added to the model by stating impact equations and Newton’s extended impact law. Both impulsive and non-impulsive motion can be gathered together in so-called equalities of measures, which are discussed in Sect. 3.4. This chapter deals with rigid multibody systems. However, the resulting equations are much more general and can also be used for the non-rigid case.