Narrow Results

The dynamical behavior of a simple pendulum hanging from a rotating arm has been investigated. The system is invariant under rotations around the axis and can be formulated as a two-degrees of freedom integrable Hamiltonian system in the absence of external forcing. The bifurcation diagram is organized around the relative equilibria (solutions that are invariant under the symmetry) and bridges connecting different bifurcation points. Special attention has been given to those solutions that could shed some light into the stabilization of the upside down solution and the control problem.