Analisis dan Visualisasi Gerak Triple Pendulum Nonlinier Menggunakan Mathematica 9

Abstract

The Program for simulation and animation of nonlinier triple pendulum motion have been done by Wolfram Mathematica software version 9. The Triple pendulum equation was derived from Lagrange equation that operated to Langrangian function. The result of the equation were plotted in graphics of the comparison of position pendulum 1 with pendulum 2, the comparison of position pendulum 2 with pendulum 3, the comparison of graphics x deviation on pendulum 1 with pendulum 2 and pendulum 2 with pendulum 3, the comparison of graphics y deviation on pendulum pendulum 1 with pendulum 2 and pendulum 2 with pendulum 3, the comparison of graphics x and y deviation’s on every pendulum, the comparison of trajectories derived by two different initial conditions, and the phase diagram of each pendulum. These Graphics were used to observe the system from periodic to chaos state. The animation of these system were given in order to show chaos state in its motion clearly. The variation that were used at animation i.e. variation angle, mass and rope length. From the experiment of this program and the exploration of dynamics in the system, it can be said that this program works well to learn chaos.