On the Issue of Collision of Balls in an Auto-Balancing Device

The paper considers a model of a vertical double pendulum, which includes two balls suspended on rigid non-deformable threads to one centre of the suspension. For the proposed system of pendulums, differential equations of motion and conditions for collision of balls have been recorded. When simulating the motion of the pendulums, the central collision of the balls has been considered for various options of the motion of the suspension point: the suspension point is motionless; the suspension point oscillates in the vertical direction; the suspension point makes rotational motions in the vertical plane. Meanwhile, various conditions for the central collision between the balls have been considered: a perfectly inelastic collision; a perfectly elastic collision; a collision with transformation of collision energy (partially elastic collision). The results of numerical simulation are consistent with the behaviour of pendulums in real physical models, which makes it possible to simulate an elastic collision between balls when studying their acceleration in auto-balancing devices.