Instability and Periodic Motion of a Physical Pendulum with a Vibrating Suspension Point (Theoretical and Experimental Approach)

摘要

In nonlinear dynamics, the motion of a pendulum represents a classical paradigm. The vibrations and stability of a pendulum with a vibrating support were studied by many authors (see, e.g., [1-12]). In spite of many publications, there were few experiments devoted to the analysis of the stability and nonlinear behavior of the pendulum. Among the well-known experimental studies, we point to the experiments made by Kapitza [1,2] in connection with the stabilization of an inverted pendulum by the high-frequency excitation of the support, as well as those made by Chelomei [3] on the stability of an inverted rod with a sliding washer under the vibrating suspension point. Experiments on the stabilization of a pendulum with a vibrating suspension point about a tilted axis were described in [4, 5]. The routes from the lower vertical position to the chaotic motion of the parametrically excited pendulum were investigated experimentally in [6]. We note that those experiments were mostly qualitative.