Pendulum with a modulated length. Part II. Regions of parametric excitation

Abstract

The first part of this paper [1] dealt with the principal peculiarities of parametric excitation of a rigid planar pendulum caused by a square-wave modulation of its length. The threshold of excitation was found and the role of nonlinear properties of the pendulum in restricting the resonant swinging was considered. In the second part of the paper the frequency boundaries of parametric instability are determined as functions of the modulation depth and the quality factor. Stationary oscillations at these boundaries are investigated.