NEUMARK-SAKER BIFURCATION IN THE PROBLEM OF INTERACTION OF A LIMITED POWER SOURCE WITH AN ELASTIC SYSTEM
The paper investigates the classical Sommerfeld problem, addressing the unbalance response of an externally damped elastic rotor, driven by a direct current motor of limited power. The motor has a linear relationship between the torque and the electric voltage in the excitation circuit. It is shown that on the plane of two parameters - the voltage in the excitation circuit and the linear damping coefficient - it is possible to distinguish a region where there are three periodic solutions, one of which is unstable. In contrast to the known results, with a small damping coefficient, the lower boundary of the region of instability of periodic motions passes from a limit point bifurcation to a Neimark-Sacker bifurcation. In the investigated case, the transition to the other (upper) stable branch occurs at low values of perturbations.