Displacement of a Rigid Body
Results concerning the motion of a rigid body between two distinct configurations are discussed in this chapter. These configurations are assumed to be finitely separated, i.e., the displacements undergone by the points of a bounded subset of the body are assumed to be finite. Infinitesimally separated configurations of a rigid body are dealt with in Chapters 3 and 4. The main results of this chapter are Euler’s Theorem, Chasles’ Theorem,the characterization of a rigid-body motion through its screw parameters, and the Aronhold-Kennedy Theorem. The concepts of screw and pose of a body are introduced, and some results concerning the displacement field of a rigid-body motion, as well as the compatibility conditions that this field verifies, are derived. Contrary to the common practice, quaternions are deliberately avoided here, the reason for such avoidance being, as explained in Chapter 1, that these require a very special algebra. One aim of this chapter is to show that rotations can be fully studied with linear algebra. The reader interested in quaternions is referred to the original works of Kelland and Tait (1882) and Hamilton (1899). A comprehensive review of the subject is given in (Spring 1986).
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