On stabilization of a triple inverted pendulum via vibration of a support point with an arbitrary frequency

Abstract

The stabilization of the upper statically unstable position of a triple inverted pendulum via parametric excitation of the support is studied. The reported results are obtained by using the multiple scale method and the Floquet theory. The stability diagrams in the excitation parameters space (amplitude and frequency of the support excitation) are plotted. It is shown that the stabilization is possible for low, medium and high excitation frequencies. The influence of the deviation of system parameters from the critical parameter, which sets the stability limit of a conservative system, and the effect of damping on the stabilization domains are discussed.