Asymptotically stable periodic orbits of a coupled electromechanical system

In this paper an electromechanical system is analyzed. The existence and asymptotic stability of a periodic orbit are obtained in a mathematically rigorous way as well as an expansion of the period by using an adequate small parameter. For the analytical results the main tool used is the regular perturbation theory. Some results, such as the growing of the period according to some powers of the parameters and the relation 2:1 between the period of the cart, which is a part of the electromechanical system, and the period of the current, are compatible with earlier numerical findings.