THE DOUBLE PENDULUM NUMERICAL ANALYSIS WITH LAGRANGIAN AND THE HAMILTONIAN EQUATIONS OF MOTIONS

A planar double pendulum is a simple mechanical system that has two simple pendula attached end to end that exhibits chaotic behavior. The aim of this research will be to numerically analyze the dynamics of the double pendulum system. First, the physical system is introduced and a system of coordinates is fixed, and then the Lagrangian and the Hamiltonian equations of motions are derived.We will find that the system is governed by a set of coupled non‐linear ordinary differential equations and using these, the system can be simulated.Finally we analyze Poincare sections, the largest lyapunov exponent, progression of trajectories, and change of angular velocities with time for certain system parameters at varying initial conditions.All numerical analysis was done using MATLAB, specifically ode45, to solve the system of 4 first-order Hamilton’s Equations of Motion

Keywords:

Hamilton’s Equations , numerical analysis , Pendulum