On the issue of the motion of balls in a double pendulum

Abstract

The paper considers a model of a vertical double pendulum with one suspension centre moving in a vertical plane. For the proposed system of pendulums, differential equations of motion and conditions for the collision of balls are obtained. When modelling the movement of pendulums, the central impact of the balls was considered for various variants of the movement of the suspension point: the suspension point oscillates in the vertical direction; the suspension point makes rotational movements in the vertical plane. In this case, various conditions of the central impact between the balls were considered: absolutely inelastic impact; absolutely elastic impact; impact with the transformation of impact energy (elastic impact). Comparison of the results of the numerical simulation and the results of experiments with the Kapitza pendulum in published sources confirmed the possibility of modelling an elastic impact between balls in a double pendulum and between balls in an autobalancer with a horizontal axis of rotation of the rotor