ABSTRACT The Dynamics of Rigid Bodies on Moving Deformable Support Media

The rocking motion of a solid block on a moving deformable base is a dynamic problem, that despite its apparent simplicity, involves a number of complex dynamic phenomena such as impacts, sliding, geometric and mate-rial nonlinearities and, under some circumstances, chaotic behavior. For that reason, since the first model proposed by G.W. Housner in 1963, a number of alternative models have been proposed for its mathematical simulation. Although, with very few exceptions, the previous models in the literature make the simplified assumption that this motion is planar, this is usually not true since a body will probably not be aligned with the direction of the ground motion. Thus, even in the case where the body is fully symmetric, the rocking motion involves three dimensional rotations and displacements. Moreover, for reasons more related to functionality than safety, it is not uncommon for heavy mechanical and electrical equipment to be placed on wheels. Examples of such devices are medical carts, mechanical equipment in hospitals, electrical transformers and recently even supercomputers. Al