Phase Bifurcations in an Electromechanical System

In this paper the dynamics of an electromechanical system is investigated. In this model, the phase of the system is a dynamical variable. The existence of four periodic orbits is proved. Two of them are asymptotically stable and the others are unstable. In the absence of viscous damping, when the parameters associated to the dimensionless voltages are adequately changed, each orbit is subject to a change of stability of the kind stable→unstable→ stable with repetition of this pattern. This phenomenon is known as Sommerfeld Effect. Moreover, the stability of these orbits depends on the zeros of the Bessel function J1.