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This paper reports and investigates paradoxical simulation results of the bouncing ball system. Chaos-like motion of the bouncing ball system with intermittent chattering (Zeno behaviour) is observed in simulations if the relative acceleration of the table exceeds a critical value. However, one can show that this is theoretically impossible. A detailed analysis is given by looking at the backward and forward dynamics of grazing solutions. It is shown in detail that a self-similar structure appears if the relative acceleration of the table exceeds the critical value.
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