Abstract
We investigate the near grazing dynamics in a slender rigid block confined between two side-walls. We obtain conditions of the existence of double grazing orbits of the system, namely, periodic orbits that have two grazing points. By extending the method of discontinuity mapping for grazing orbit with a single grazing point, we compute the lower and the higher order approximations of the Poincaré map respectively near the double grazing orbit. The results of computing Monte Carlo bifurcation diagrams obtained by the lower and the higher order maps respectively are compared with those from direct simulations of the original system. We find that there are large disagreements between the lower order map and the original system. Thus the lower order map is not accurate enough to study double grazing bifurcations. On the other hand, the higher order map can effectively reduce such disagreements and we expect that it plays an important role in the study of the near grazing dynamics of the system.
Published Version
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