Stabilizing the oscillations of a controlled mechanical system with $n$ degrees of freedom

A mechanical system with n degrees of freedom subjected to the action of positional forces and a small smooth control is considered. It is assumed that in the absence of control, the system may have a family of single-frequency oscillations. A universal control—a nonlinear force that implements and simultaneously stabilizes a cycle in the system—is found. An illustrative example is given. In the previous paper [5], the universal control was designed for a two-dimensional manifold of the system.