Construção e caracterização dinâmica de um pêndulo duplo caótico

Abstract

In this work an electromechanical system that exhibits sensisitive dependence on initial conditions is built and dynamically characterized. The system is comprised by a double pendulum connected to a DC motor that is used to exert momentary torque impulses on the mechanism. The torque impulses are produced according to the values of system state variables, and therefore the system can be considered to be autonomous. The only measured variable is the double pendulum first bar angular rate, which is used to evaluate the system dynamical behavior through delay coordinates state space reconstruction. Various techniques, such as the evaluation of the largest Lyapunov exponent and the estimation of the correlation dimension are employed to analyse simulated and measured time series from the electromechanical double pendulum. The results obtained so far indicate that the system is indeed chaotic.