Quenching in a class of singularly perturbed mechanical systems

In this paper we get some results about the dynamics of a class of mechanical systems under strong dissipation. We have obtained the stability of the semi-trivial solutions in this class, its asymptotic expansion, and the existence of hyperbolic periodic orbits and their stability was analysed. From these results we have showed the existence of quenching in a particular case. ► Results on the dynamics of mechanical systems under strong dissipation are obtained. ► The problems are approached by using singular perturbation theory. ► A new result on asymptotic expansions is obtained. ► It is obtained a rigorous result on quenching of a class of mechanical systems.