Parametric resonance induced chaos in magnetic damped driven pendulum

TL;DR

This paper investigates how parametric resonance can induce chaos in a magnetic damped driven pendulum, combining theoretical analysis, numerical simulations, and experiments to understand the complex dynamics.

Contribution

It provides a novel analysis of chaos triggered by parametric resonance in a magnetic pendulum system, supported by theoretical, numerical, and experimental evidence.

Findings

Chaos occurs at specific parametric resonance conditions

Analytical results align with numerical simulations

Experimental validation confirms theoretical predictions

Abstract

A damped driven pendulum with a magnetic driving force, appearing from a solenoid, where ac current flows is considered. The solenoid acts on the magnet, which is located at the free end of the pendulum. In this system, the existence and interrelation of chaos and parametric resonance is theoretically examined. Derived analytical results are supported by numerical simulations and conducted experiments.