Abstract
A simple piecewise linear forced oscillator with impacts is taken as a model for more complicated vibro-impacting systems. The presence of impacts makes the system discontinuous and non-linear and to study it effectively the theory of dynamical systems is used. By a combination of analytical and numerical techniques, many phenomena are identified which are characteristic of non-linear dynamical systems as the system parameters are varied. In particular, these include chaotic regimes and multiply coexisting stable states. The domains of attraction of the periodic states are plotted and compared with the strange attractors of the chaotic states. In addition, phenomena are observed related to the discontinuity which have no counterpart in smooth dynamical systems; chatter, when infinitely many impacts occur in a finite time, and grazing, when a stable periodic orbit encounters a discontinuity and disappears catastrophically under a smooth change in the parameters.
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