Vibrations of a Pendulum with Oscillating Support and Extra Torque
  The motion of a driven planar pendulum with vertically periodically oscillating point of suspension and under the action of an additional constant torque is investigated. We study the influence of the torque strength on the transition to chaotic motions of the pendulum using Melnikov's analysis. 
Marek Borowiec, Grzegorz Litak and Hans Troger