Dynamics of Pendulum Forced by a Magnetic Excitation with Position-Dependent Phase

TL;DR

This paper explores the complex dynamics of a magnetic pendulum influenced by a position-dependent phase magnetic excitation, revealing multistability, bifurcations, and chaos through combined simulations and experiments.

Contribution

It introduces a novel mathematical model incorporating position-dependent phase in magnetic excitation and validates it with experiments, advancing understanding of magnetic pendulum dynamics.

Findings

System exhibits multistability and chaotic behavior.

Bifurcation analysis confirms complex dynamical regimes.

Experimental results align well with simulations.

Abstract

This study investigates the dynamics of a magnetic pendulum under time-varying magnetic excitation with a position-dependent phase. The system exhibits complex chaotic and regular dynamics, validated through simulations and experiments. The mathematical model, based on a physical setup, includes a magnetic excitation torque with phase dependence on the dynamic variable. Bifurcation analyses confirm the rich multistability of the system, showcasing periodic attractors, period-doubling bifurcations, and chaotic behavior. Experimental validation demonstrates a high agreement between numerical and experimental results, supporting the efficacy of the proposed model. The study sheds light on the system's sensitivity to changes in magnetic interaction, providing insights into controlling resonance energy exchange in coupled magnetic pendulum systems.