Dynamics of a Two-Pendulum Model with Impact Interaction and an Elastic Support

This paper examines the dynamic behavior of a double pendulummodel with impact interaction. One of the masses of the two pendulumsmay experience impacts against absolutely rigid container wallssupported by an elastic system forming an inverted pendulum restrainedby a torsional elastic spring. The system equations of motion arewritten in terms of a non-smooth set of coordinates proposed originallyby Zhuravlev. The advantage of non-smooth coordinates is that theyeliminate impact constraints. In terms of the new coordinates, thepotential energy field takes a cell-wise non-local structure, and theimpact events are treated geometrically as a crossing of boundariesbetween the cells. Based on a geometrical treatment of the problem,essential physical system parameters are established. It is found thatunder resonance parametric conditions of the linear normal modes thesystem's response can be either bounded or unbounded, depending on thesystem's parameters. The ability of the system to absorb energy from anexternal source essentially depends on the modal inclination angle,which is related to the principal coordinates.