Result: Simulation of Chaotic Operation οf A Damped Driven Pendulum Using Python

In this paper, we are presenting a new pedagogical method for the introduction of the study of nonlinear systems. Our approach is based on the use of open-source software which is publicly available. In response to this motivation, we are using the Python programming language which offers a holistic approach to scientific research. We will present the analysis of the pendulum motion under the influence of an external force. The differential equation governing the system will be presented and solved using numerical methods. Moreover, the phase diagram of the system will be presented for various system parameters. We will describe the transition to a chaotic operation and the key factors of this procedure. The chaotic behaviour is verified by calculating the maximum Lyapunov exponent. This pedagogical approach emerging is based on the physical properties of the system and not on the numerical methods used so that the student can understand the dynamics of the system more comprehensively.