This project will concentrate on three targets. The first consists in an analytical and numerical approach to the dynamics of rigid body systems in the presence of friction forces; dynamics of kinematic couples with large clearances; dynamics of two-wheel carts; asymptotic motion of systems with varying friction phenomena. The second concerns the study of dynamics of systems of rigid and deformable bodies, stability and control: development of algorithms for control and stabilization of mechanical systems; stability of non-holonomic stems; applications to large satellite systems and road vehicles; the control and reorientation of satellite systems with rotors (gyrostats); existence and stability of steady motions for large flexible systems and tethered satellites; stability of vehicles including trailers. The last one is related to the infinite dimensional dynamical systems: applications of asymptotic methods to systems containing viscoelastic elements; satellites with cavities partially filled with liquids.