Stabilization of the Classical Shimmying Wheel

Many vehicle systems contain rolling elements which exhibit unstable rolling motion, called shimmying, which may lead to disastrous results. The classical shimmying wheel is a simple model which captures the essential dynamics of such systems. Fortunately, this model possesses a particular geometric structure which provides a simple means to design a globally stabilizing controller. However, this model is limited because it assumes that the wheel rolls without slipping, and for real systems, the wheel may slip because the constraint force, applied by friction, is bounded. The controller which globally stabilizes the rolling system sometimes fails to stabilize the slipping system. An alternative control strategy is proposed which is more e ective in stabilizing the slipping system.