Independent Asymmetric Period-3 Motions in a Periodically Forced Double-Pendulum

In this paper, the independent asymmetric period-3 motions of a periodically forced, damped, double-pendulum are predicted through a discrete implicit mapping method. The corresponding stability and bifurcation conditions of the paired asymmetric period-3 motions are determined through eigenvalue analysis. Numerical simulation of the two asymmetric period-3 motions in the double-pendulum system is completed from analytical predictions. The example presented herein can be used for the vibration reduction of the first pendulum through the motions of the second pendulum.