On the asymptotic behavior of mechanical systems with friction

We study the asymptotic behavior of systems with the Coulomb friction expressed as Lagrange's equations of the second kind with solutions in the sense of Filippov. The friction coefficients are assumed to have dependence on generalized states, velocities, and time which can arise for various reasons such as temperature change, surface roughness, and other characteristics of the rubbing bodies. Combining the direct method of Lyapunov functions with semidefinite derivatives and the method of limit equations stemming from the works of Sell (1967) and Artstein (1977, 1978) on the topological dynamics of nonautonomous systems, we construct the limit differential inclusions by the methods of set-valued analysis and the theory of discontinuous systems.