Homoclinic and heteroclinic bifurcations of the motion of rotating pendulum

Abstract

The goal of this work is to investigate the nonlinear oscillations of the forced, damped rotating pendulum. When the damping coefficient and the amplitude of the excitation force are zero, the system is autonomous with an explicitly known homoclinic and heteroclinic orbits. The homoclinic and the heteroclinic orbits are calculated. Melnikov functions due to the homoclinic and the heteroclinic orbits are calculated to detect the transverse homoclinic and heteroclinic orbits. Regular and chaotic motions are shown to be possible in the damped case. Numerical methods are used to obtain time history, phase portrait, Laypunov exponents, Poincare' maps and their fractal dimensions.