Universal bifurcations in impact oscillators

We give experimental evidence for a new bifurcation structure that arises when smooth dynamical systems cross a boundary. Our experiment concerns a driven impacting leaf-spring oscillator with a very precise control of the driving amplitude. The results are in surprisingly good agreement with the predictions of a simple nonlinear mapping that is valid near grazing impact (i.e. impact with zero velocity). The agreement is surprising because a multitude of vibration modes of the spring is excited upon impact whereas the mapping is two-dimensional. Additionally, we consider the case where the impact is not instantaneous due to collisions with a nonrigid stop. This case can be captured by a mapping and we find strong support for the universality of impact phenomena, even in systems that have nonidealities