Investigating the pathway to chaos in a simple pendulum

Abstract

The path to chaos in a simple pendulum was investigated in this research work. The equations governing three states of motion of the simple pendulum–undamped, damped and force-driven states were solved numerically using the Runge-Kutta method of the fourth order. The phase space plot of the system obtained using Java programming language was analysed and the fixed points were determined using the Jacobian matrix. The stability of the fixed points was also determined.The simple pendulum was found to be non-chaotic in the undamped state, attenuate in the damped state and approach chaos as the forcing parameter in the equation of the system was gradually increased.