NUMERICAL SIMULATION OF THE CHAOTIC BEHAVIOUR OF A THREE-DIMENSIONAL PENDULUM

Abstract

A nonlinear pendulum is designed to demonstrate the chaotic instability of trajectories. Here, we present a simplified theoretical description of its dynamics. Trajectories are found by numerical integration of the Lagrange equations. The results of the simulations agree with the Poincar´e-Bendixon theorem. Generic trajectories display chaotic behaviour and are similar to those obtained experimentally

Keywords

• chaos
• dynamical systems