Dynamics of a horizontal pendulum driven by high-frequency rocking

This paper investigates the dynamics of a horizontal pendulum subjected to high frequency rocking. The method of direct partition of motion is applied to the governing equation to separate the fast and slow dynamics. It is shown that two stable equilibria may coexist for certain parameter values. It is also shown that the high frequency excitation can stabilize an unstable equilibrium for a horizontal pendulum driven by a rocking motion. The aforementioned theoretical results show good agreement with numerical investigations. A series of experimental tests were also performed to corroborate the bifurcation threshold where forcing parameters can cause a change in stability.