Oscillatory control of bifurcations in rotating chains

Recent literature has addressed the issue of using high-frequency periodic inputs in the open-loop stabilization of mechanical systems. Equilibria and their stability are found by averaging the Hamiltonian and then studying critical points of the resulting averaged potential. In this paper, we consider the stabilization of undeflected hanging modes of n-link planar kinematic chains by high frequency vertical forcing. We show that the effect of the periodic forcing is to postpone a bifurcation in which the hanging equilibrium of this chain system becomes unstable. This work has been motivated by a number of laboratory experiments in which a variety of applications of periodic forcing have been observed to produce significant stabilizing effects