The intermediate frequency effect and Dzhanibekov-like transitions in the response of the anisotropic pendulum

Abstract In this work the free vibration response of the anisotropic pendulum is analyzed. The spherical pendulum has three primary periodic motions of free vibration, but two are degenerate and have the same frequency, and therefore all three are stable. In contrast, the anisotropic pendulum has three distinct primary periodic motions of free vibration, but only if the level of energy is above a critical threshold. In this case, the primary periodic motions have distinct frequencies. It is show