Research on the nonlinear dynamical behavior of double pendulum

The paper studied nonlinear dynamical behavior in a double pendulum system by Lagrange's method and numerical computations. First, it introduced the physical system, and then derived the Lagrange and the Hamiltonian equations of motions. Finally it analyzed Poincare sections, the largest Lyapunov exponent, progression of trajectories, and change of angular velocities with time for certain system parameters at varying initial conditions. The results of numerical simulation show that the system will have the possibility of chaos when the initial condition is changed. The results provide references for detailed research on dynamic characteristics and optimal design of the double pendulum model.