Double pendulum induced stability

In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa?s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy ? positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments