ABSTRACT
The bouncing ball problem has been very investigated (Mello & Tufillaro 1987; Mehta & Luck 1990; Luck & Mehta 1993; Bellomo & Uzer 1994). A vertical sinusoidal vibration excites a ball on a plate. If the ball is initially at rest, the ball stays in contact with the plate while the maximum acceleration of the plate is lower than the gravity g. By increasing the amplitude of the plate oscillations, the acceleration becomes sufficient to lift off the ball. The collision of a ball with a plate is characterized by a restitution coefficient ε, i.e. the ratio between the speed after and before the hit. The vibrating plate may provide the speed lost by the shock and an excited state that is periodical and stable is obtained. The ball is then excited and bounces at the same frequency as the plate and at a given phase. Increasing the amplitude of the vibration, the ball may bounce at twice the period of the plate (second excited state).At large amplitude of the excitation, the ball bounces randomly and a chaotic behavior is observed. This system constitutes a paradigm of the chaos generator (Tufillaro et al. 1992).
