CHATTERING AND RELATED BEHAVIOR IN IMPACT OSCILLATORS

One of the most interesting properties of an impacting system is the p ossibility of an infinite number of impacts occurring in a finite time (such as a ball bouncing to rest on a table). Such behaviour is usual ly called chatter. In this paper we make a systematic study of chatter ing behaviour for a periodically forced, single-degree-of-freedom impa ct oscillator with a restitution law for each impact. We show that cha tter can occur for such systems and we compute the sets of initial dat a which always lead to chatter. We then show how these sets determine the intricate form of the domains of attraction for various types of a symptotic periodic motion. Finally, we deduce the existence of periodi c motion which includes repeated chattering behaviour and show how thi s motion is related to certain types of chaotic behaviour.