Dynamics of a pendulum with a quasiperiodic perturbation

The dynamics of a damped pendulum with a quasiperiodic external perturbation is investigated. It is shown that in contrast to a pendulum with a periodic perturbation, a quasiperiodic perturbation leads to chaos in the weakly nonlinear limit when the peak-to-peak amplitude of the oscillations of the pendulum is small. This effect is attributed to the appearance of saddle states induced by the external perturbation. The analytical conditions for the appearance of chaotic oscillations are obtained by the method of running Lyapunov exponents and by the repeated-averaging technique. Zh. Tekh. Fiz. 67, 1–7 (October 1997)