On the qualitative behaviour of nonlinear oscillators with dry friction

Modelling oscillations with dry friction we get ordinary differential equations with discontinuous right hand side. An example for such oscillating systems is the pendulum equation phi double over dot + g(phi over dot - omega(0)) sgn(phi over dot - omega(0)) + f(phi) = A(omega t), where phi represents the angle of the oscillating system, phi over dot - omega(0) the relative velocity, g(.) sgn(.) the friction force, f(.) the restoring force and A(.) a periodic forcing. Such nonsmooth systems we can. model by differential inclusions of Filippov type. We will study some qualitative properties of such systems.