Dynamics of a two-pendulum model with impact interaction and an elastic support

This paper examines the dynamic behavior of a double pendulum model with im pact interaction. One of the masses of the two pendulums may experience imp acts against absolutely rigid container walls supported by an elastic syste m forming an inverted pendulum restrained by a torsional elastic spring. Th e system equations of motion are written in terms of a non-smooth set of co ordinates proposed originally by Zhuravlev. The advantage of non-smooth coo rdinates is that they eliminate impact constraints. In terms of the new coo rdinates, the potential energy field takes a cell-wise non-local structure, and the impact events are treated geometrically as a crossing of boundarie s between the cells. Based on a geometrical treatment of the problem, essen tial physical system parameters are established. It is found that under res onance parametric conditions of the linear normal modes the system's respon se can be either bounded or unbounded, depending on the system's parameters . The ability of the system to absorb energy from an external source essent ially depends on the modal inclination angle, which is related to the princ ipal coordinates.