Periodic and falling-free motion of an inverted spherical pendulum with   a moving pivot point
  For the system of an inverted spherical pendulum with friction and a periodically moving pivot point we prove the existence of at least one periodic solution with the additional property of being falling-free. The last means that the pendulum never becomes horizontal along the considered periodic solution. Presented proof is an application of some recent results in the fixed point theory. 
Ivan Polekhin
math.DS math.CA