Chelomei's problem of the stabilization of a statically unstable rod by means of a vibration

Chelomei's problem of the stabilization of an elastic, statically unstable rod by means of a vibration is considered. Formulae for the upper and lower critical frequencies for the stabilization of the rod are obtained and analysed. It is shown that, unlike the high-frequency stabilization of an inverted pendulum with a vibrating suspension point, a rod is stabilized by frequencies of a periodic force of the order of the fundamental frequency of the transverse oscillations of the uncompressed rod lying in a certain range.