A driven system of impacting pendulums: Experiments and simulations

This paper studies a system composed of two pendulums attached to a common base that is oscillated horizontally. The pendulums share a common pivot line, but move independently and are only coupled together through collisions. Impact dynamics for the collisions of the pendulums with each other and with fixed barriers yield complex nonlinear behaviors. Careful numerical simulation of the equations of motion demonstrates a close correlation with experimental data collected from the system. There are many independent parameters in this system, and one of the motivations for the present study is to establish the extent to which we can capture observed behavior with a relatively simple hybrid differential equation model in the face of several independent energy dissipation mechanisms coming from friction and impact. Comparison between experiments and simulations is based on the standard nonlinear dynamical system analyses of time series, phase projections, time-lag embedding, Poincaré sections, and frequency content. Grazing bifurcations and co-existence of impacting/non-impacting periodic/chaotic states are observed.