This work deals with three-dimensional (3D) modeling of container cranes including the hoisting cable length commands. The proposed models allow to effectively study the 3D motion caused by the eccentricity of initial conditions or loading conditions such as those induced by wind. The container is modeled as a 3D rigid body while the hoisting cables are treated either as inextensible trusses or as linearly elastic straight, taut cables. The 3D model with inextensible cables is shown to coalesce into existing two-dimensional models under the relevant planarity constraints. Details about the treatment of the internal inextensibility constraints are discussed. Time-marching simulations are carried out to show representative 2D and 3D responses to initial conditions and commanded motion of the trolley. The main differences between the constrained model and that with the elasticity of the cables are highlighted in the framework of a few significant design scenarios.

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