Time dependent forces and stability of equilibrium for holonomic systems

This paper concerns some results on stability of the equilibrium position of holonomic mechanical systems subject to a generalized conservative force and a dissipative one by means of families of Lyapunov functions. The most interesting results concern the case in which the generalized conservative force is the product of a conservative force and a function f(t) periodic in t. In this case we obtain asymptotic stability even if when there is instability for f(t)=1.