Dynamical complexities of forced impacting systems

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Abstract
The model of a forced linear oscillator with instantaneous impacts at one or two stops is discussed. The nonlinearities introduced by the instantaneous impact rule are sufficient to cause typical nonlinear behaviour. The impact rule is discontinuous, introducing discontinuities into discrete time Poincaré maps defined from the continuous time dynamical system. Discontinuities also exist in the derivatives of these maps. The implications of these discontinuities are discussed and their relevance to engineering applications is assessed with suggestions for further research.