Inverted dynamics of a tilted parametric pendulum

We consider here the dynamics of a planar pendulum whose pivot points is rapidly forced with a periodic driving. We focus attention on stable `inverted' motions which exist on, or close to, the upright position. Following earlier studies, the initial emphasis is placed on the system with vertical sinusoidal forcing while the later results correspond to excitation which has an additional horizontal component. In particular we examine the nature of the stable inverted solution as the symmetry is broken via numerical investigations. Finally, some remarks are made on the physical significance of the results.