Synchronization Dynamics in Multi-Mass Pendulum Systems

Abstract

In this work, a computational study is presented on the synchronization phenomenon between two compound pendulums with multiple masses, mounted on a mobile platform subjected to external periodic forcing. The platform plays a dual role: it acts both as an energy supply source and as a coupling medium between the pendulums, enabling energy exchange and facilitating synchronization. The mathematical model of the system is formulated by considering the interaction between the pendulums and the supporting structure. Numerical simulations are carried out to analyze different pendulum configurations, in which a control action is applied to one pendulum with the aim of inducing its stable rotation. The study then evaluates whether, through synchronization, such a condition can be transmitted to the other pendulum. The use of basins of attraction and temporal response diagrams allowed corroborating the interaction between the pendulums through the supporting structure, and how an electromagnetic control action affected the probabilities of obtaining synchronized responses between the pendulums.