Complete Bifurcation Analysis of a Pendulum with a Vibrating Support

It is known, that behavior of a periodically driven damped pendulum may be very complex and sometimes with the unexpected phenomena such as stable hilltop vibrations, complex subharmonical and quasi-periodical vibrations, and different rotations [1-6]. In this paper we investigate global dynamics of a more common model then the models used in the usual previous investigations. Three cases are under consideration: a) with horizontal excitation of the vibrating support, b) with vertical excitation, c) with excitation under some angle α from the horizontal direction