Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation

In this study, we investigate the dynamics of an inverted pendulum subjected to high-frequency excitation. In particular, we focus on bifurcation phenomena in the dynamics and analyze the effect of the tilt of the excitation direction with respect to gravity direction on the bifurcation. It is analytically clarified that the tilt produces stable equilibrium states different from the directions of the gravity and the excitation. The stability of the stable equilibrium states under the effect of the tilt is discussed non-locally. Also, an analogy of the bifurcation of the inverted pendulum to that of the buckling phenomenon is presented. The theoretically predicted effects of the tilt are qualitatively confirmed by performing some experiments.