Motion in Three Dimensions

This chapter treats the fully three-dimensional dynamic response of rigid bodies. Although most undergraduate courses do not cover this topic, it is a natural evolution of the approach advocated in this book. The derivations, based upon the typical particle construction, follow along the same path first developed in earlier chapters. The main challenge of dynamics in three dimensions is dealing with rotations, which we do exclusively through Rodrigues’ formula for rotation in three dimensions. The chapter ends with a few codes that show how to deal with rotation in the context of numerical computations.