Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator

We consider the rising phenomena which occur in sticking solutions of a two-degree of freedom impact oscillator. We describe a mathematical formulation for modelling such a systems during both free flight and during sticking solutions for each of the masses in the system. Simulations of the sticking solutions are carried out, and rising events are observed when the forcing frequency parameter is varied. We show how the time of sticking reduces significantly as a rising event occurs. Then within the sticking region we show how rising is qualitatively similar to the multi-sliding bifurcation for sliding orbits.