THE MOTION OF A MASS HANGING FROM AN OVERHEAD CRANE

We study the dynamics of a mass hanging from an overhead crane whose p ulley support undergoes a small vertical oscillation. Firstly, we use Lagrangian mechanics to derive a differential equation describing the motion of the crane system and then we reduce the equation in three pa rticular cases by making certain assumptions about the motion of the s ystem. In one of these cases, we use Melnikov theory to establish the existence of both chaotic and subharmonic periodic solutions of the cr ane system, for particular parameter values.