A rotary tower crane system: an appealing problem in nonholonomic mechanics

Abstract

ABSTRACT Cranes system is widely used to transport heavy loads and hazardous materials in shipyards, factories, nuclear installations and high-building construction and plays an important role in the production process and serves to transfer loads from one place to another. Cranes are the best way of providing a heavy lifting facility covering virtually the whole area of the industry. The equations of motion of a rotary tower crane are highly non-linear, and rolling without slipping condition of the trolley on the jib plane can only be expressed by nonholonomic constraint equations. In this paper, a geometrical theory of general nonholonomic constrained systems on fibred manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was applied to the above-mentioned mechanical problem. The dynamical model is preserved in simulations in its original non-linear form without any simplification. The results of numerical solutions of constrained equations of motion, derived within the theory, open the possibility of direct application of the theory to practical situations.