Modelling and Analysis of Bifurcation Dynamics of Two Coupled Pendulums with a Magnetic Forcing

Abstract

The paper presents a novel mechatronic system comprised two flexibly coupled pendulums forced by a repulsive magnetic field. The dynamics of the system is investigated theoretically and experimentally. General equations of motion including magnetic interaction are derived as well as the potential energy of the system is presented. Bifurcation analysis proves presence of periodic, quasi-periodic and chaotic types of the system motion. Chaotic attractors and their neighboring regular responses are shown, coexisting of the regular attractors is detected too and basins of attraction for these regular solutions are calculated numerically in terms of initial conditions.