Numerical and experimental study of dynamics of two pendulums under a magnetic field

Abstract

In this article, a two-degree-of-freedom system consisting of two pendulums with magnets embedded in a variable magnetic field is investigated experimentally and numerically. Pivots of the pendulums are coupled by an elastic element. The magnetic interaction originates from permanent magnets, mounted at free ends of the pendulums and current-powered air coils underneath. A novel model for the magnetic force is proposed and verified experimentally. Nonlinear dynamics of the system is examined by means of time series, bifurcation diagrams, phase portraits, and Poincaré sections. Regions of chaotic and regular motion are predicted numerically and justified experimentally. Multiperiodic motion and coexisting solutions are detected, and pictures in basins of their attraction are reported, among other.