Rocking instability of a pulled suitcase with two wheels

Rocking motions of a two-wheeled suitcase are considered. The suitcase is pulled on a horizontal ground and may rock back and forth, first with one wheel in contact with the ground, then the other, and so on. When a wheel impacts the ground, some energy is lost. It is assumed that the puller's walking motion induces a periodic force or moment on the handle of the suitcase. In addition, the puller may apply an additional restoring moment in an attempt to suppress the rocking motion. Under certain conditions, the motion may grow until the suitcase overturns. The effects of the excitation frequency and the coefficient of the restoring moment on the critical excitation amplitude are examined for the special case in which yaw and pitch motions are neglected and the suitcase is pulled in a straight line. Due to the nonlinearities of the problem, the results exhibit some irregular behavior.