Motion control of a bridge crane with a load by finding its acceleration

A possible approach to controlling a bridge crane motion while moving cargo is considered. Two different methods for finding the controlling acceleration that providing vibration damping of the cargo being carried are suggested. The first of these methods is based on applying classical Pontryagin maximum principle. The second method, using generalised Gauss principle, is based on modern researches in nonholonomic mechanics. The new method relies on the results of applying the classical one and can be used as independent approach for solving various problems of control.