Approximations for Almost-rigid Bodies

If for all motions in a certain class the deformations of a body are small enough to be ignored, then relative to this class we say the body is rigid. The assumption of rigidity is an idealization that has given rise to a large body of work in mechanics. Nevertheless, there are also important problems in which the effects of deformation, while still quite small, cannot be ignored. For motions of this type we say the body is nearly rigid. Approximations for nearly rigid bodies have technological implications both old and new. Historically, the gyroscopic motion of the earth has always fascinated and challenged astronomers and geophysicists. This motion exhibits special complexities owing to the fact that the earth is not exactly rigid. An indication of the scope of work in this area can be found in the treatise of Lambeck [1980]. More currently, problems arise in space technology where the control of orbital motions of space vehicles and satellites is paramount. Complexities arise here from the flexibility of the satellite and accompanying elastic oscillations and rotational perturbations. The analysis of such problems involves rather ingenious modeling and large-scale numerical computations. The work of Williams [1976] provides an indication of the state of the art in the field.