Experimental investigation of some consequences of low velocity impacts in the chaotic dynamics of a mechanical system

Abstract

An experimental investigation of an impacting system is presented. The dynamical behaviour of the experimental system is compared with that of a simple model system using the common notion of an instantaneous velocity change, with outgoing velocity being a function of incoming velocity. This type of model has singularities in the Poincaré mappings used to describe the dynamics and this produces effects not found in smooth dynamical systems. The major contribution of this study is to show that these effects are also characteristic of the experimental system. One of those effects is that the chaotic attractors exhibit certain geometric features. The accuracy of the measurements made it possible to identify this effect in the experiment. As the experimental system is more complicated than the model, our measurements support that these features are present in more complex models. Thus it is demonstrated that the geometric features provide a diagnostic tool for impact studies.