A Parameter-Driven Approach to Synchronize Single and Double Pendulums Using the Kuramoto Model for Real-World Applications

This paper investigates the relationship between single and double pendulum synchronization and real-world synchronization. The Kuramoto model was applied to couple single pendulums and the results were analyzed for implementing double pendulum synchronization. A differential equation approach was utilized to model N double pendulums, and an ordinary differential equation solver was implemented in Python. Double pendulum oscillations were modeled using the Lagrangian equations of motion due to the constraint-independent benefits. Investigation outcomes were utilized to explain synchronization phenomena in real-world dynamical systems: lockstep, Galilean moons, Centaurus A, Belousov-Zhabotinsky reaction. Single pendulum synchronization was achieved with sufficient coupling power K. Double pendulum synchronization was achieved with a sufficiently small initial displacement from equilibrium, stable constants for mass and length, and sufficient coupling strength K. The results yield the possibility of phase-shifted synchronization for chaotic systems contingent upon the system's ability to overcome state-dependent chaos.