Extracting information from interimpact intervals in a mechanical oscillator

Monitoring all the state variables in dynamic experiments may be difficult or even impossible. It is also desirable to reduce the coupling between the system under study and the measuring device to as low a level as possible. To these ends, we investigated the use of interimpact interval as a discrete state variable. It is well established that topological information can be obtained from delay coordinate embedding and thus not all of the state variables, or even a continuous set of a single variable, need to be measured. In the case of impacting systems, the impacts can be viewed as discrete events that can then be used to reconstruct more general features of the behavior. The success of such reconstruction techniques will be assessed in this paper.