Mappings of grazing-impact oscillators (Q2712982)

Impacting systems can be found in a variety of mechanical constructions, and they are intrinsically nonlinear. The authors show that systems in which the impacts take place at low speed can be described by discrete mappings. They deal with the case of a harmonic oscillator in detail. The map for impacts with a compliant obstacle is very similar to the one describing collisions with a rigid obstacle. A notable difference is a change of scale of the bifurcation parameter. The authors illustrate their findings in the limit of large damping, where the mechanism of period adding can be analyzed exactly. The relevance of the results to experiments on practical impact systems is indicated.