On the dynamics of a vertically driven damped planar pendulum

Results on the dynamics of the planar pendulum with parametric vertical time-periodic forcing are reviewed and extended. Numerical methods are employed to study the various dynamical features of the system about its equilibrium positions. Furthermore, the dynamics of the system far from its equilibrium points is systematically investigated by using phase portraits and Poincare sections, The attractors and the associated basins of attraction are computed. We also calculate the Lyapunov exponents to show that for some parameter values the dynamics of the pendulum shows sensitivity to initial conditions.