Odeling and simulation of chaotic system through coupled pendulums using SimMechanics Simulink

Abstract

This article examines the case of a double and a triple pendulum, as simple examples of a physical system can exhibit chaotic behavior. Using the Lagrange formalism for differential equations of motion associated with the angles θ1, θ2 and θ3 respectively, are determined that these differential equations are found to be second order ordinary nonlinear and coupled, which are solved numerically using Matlab. We develop a model in Simulink to represent the motion of the system using animation in real space, which is achieved by directly analyzing and describing the system behavior in terms of the relevant parameters are the masses and the lengths of the pendulums .For each case investigated are graphs that account for how they behave the angles θ1, θ2 and θ3 function of time. The figures are presented, corresponding to the animations for a time of 40-80 seconds, showing theactual paths followed by each of the pendulums, noting that the latter canperform both rotary and oscillatory motions, accounting for this form of the complexity of the movement. Also in these figures show the obvious changethat occurs in the system's behavior by changing the lengths.