Stability and attractivity of mechanical systems with unilateral constraints

In this paper we will give conditions under which the equilibrium set of multi-degree-of-freedom nonlinear mechanical systems with an arbitrary number of frictional unilateral constraints is attractive. The theorems for attractivity are proved by using the framework of measure differential inclusions together with a Lyapunov-type stability analysis and a generalisation of LaSalle’s invariance principle for non-smooth systems. The special structure of mechanical multi-body systems allows for a natural Lyapunov function and an elegant derivation of the proof. These results are illustrated by means of examples with unilateral frictional constraints.