Chaotic motions in the resonant separatrix band of a parametrically excited pendulum

摘要

The energy increment spectrum method is developed for the numerical prediction of the appearance and disappearance of a primary (2M : 1)-librational or (M : 1)-rotational resonant separatrix band in a parametrically excited pendulum. The analytical conditions for the presence of such separatrix bands are also obtained. Illustrations of the analytical and numerical results for the appearance and destruction of the resonant bands are given for a comparison.