The Stephenson - Kapitsa pendulum: Area of the Attraction of the Upper Positions of the Balance

Abstract

Here we consider the behavior of a pendulum with a vibrating axis of suspension which differs from the classical one by the presence of an additional degree of freedom: the pendulum contains some mass, fixed on a spring, which can be displaced with respect to the main mass in two mutually perpendicular directions. Experimental investigations have been performed to determine the stable equilibrium positions of the pendulum. The results of the experiment were in good agreement with those of the numerical solution of the complete equations of motions of the system. Both of them were in good agreement with the rough analytical solution, obtained before by I.I. Blekhman and L. Sperling. It has been confirmed that the presence of the inner degree of freedom of the additional mass in the “radial” direction results in an essential widening of the range of attraction of the upper vertical quasi-equilibrium position of the pendulum