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For the system of an inverted spherical pendulum with friction and aperiodically moving pivot point we prove the existence of at least one periodicsolution with the additional property of being falling-free. The last meansthat the pendulum never becomes horizontal along the considered periodicsolution. Presented proof is an application of some recent results in the fixedpoint theory.

Periodic and falling-free motion of an inverted spherical pendulum with a moving pivot point