On motion of a spatial rod system containing a gyrating rotor (Q2735910)

The spatial motion of the flat double-hinged pendulum is considered. A link contains a rotating rotor. The motion equations are obtained in the form of the Lagrange equations of the second kind. These equations at operation with balancing moments admit a particular solution for which the pendulum is fixed in the vertical plane and the rotor makes uniform rotations. In a neighborhood of this solution the system is linearized, the respective equation and formulas for evaluation of its radicals are obtained. The positions of the upper and lower equilibrium are considered and their stability is investigated using linear approximation. Under the assumption that this system is under the action of the control moment on all states it is shown that the linearized system is controllable. Therefore, the nonlinear system has the same property. If the moment acts only on a rotor then the linearized system is uncontrollable and the possibility of control and stabilization of equilibrium positions should be established by nonlinear methods.