Bifurcations in a horizontally driven pendulum

We consider a forced pendulum with a horizontally oscillating suspension po int. Bifurcations associated with stability of the symmetric period-1 orbit (SPO), arising from the "unforced" stationary point, are investigated in d etails by varying the two parameters A (the normalized driving amplitude) a nd Omega (the normalized natural frequency). We thus obtain the phase diagr am showing the bifurcation curves of the SPO in the Omega - A plane through numerical calculations of the Floquet (stability) multipliers and winding numbers. We note that a specific substructure in the bifurcation set of the SPO recurs in the parameter plane.