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