Chaotic behaviors and multiple attractors in a double pendulum with an external harmonic excitation

In this paper, the dynamic behavior of a double pendulum under horizontal harmonic excitation is studied. The mathematical model is described by a four-dimensional non-autonomous system with smooth nonlinearities. Based on the sensitivity analysis of parameters, two representative parameters are selected and their influences on the system behavior are reported with a set of high-resolution stability diagrams. In addition to explore the classical dynamic behavior of the system, our study also investigates the issue of multistability arising from attractor self-reproducing. To enhance the reliability of our findings, simulations were conducted within a multi-body simulation environment, which yielded consistent and robust results. Furthermore, utilizing the experimental platform developed with Qualisys, we identified several pairs of attractors with specific offsets, a significant indication of attractor self-reproducing. This paper will contribute to understand the rich and intriguing behaviors of the double pendulum.