Kinematics of Rigid Body Motion

We recall that a body B is a collection of material points P: = B = {P}. In general, all of the particles of a body may change their relative positions in B. and in this case the body is said to be deformable. At the other extreme, a rigid body is a body with the property that the straight line distance between every pair of its particles is constant in time. This idealization of a body that cannot be deformed, however great may be the forces and torques that act upon it, is so intuitively natural that it is often used without mention. The reader surely will recognize that our basic definition of a reference frame embodied the concept of rigidity. In fact, there were several occasions in Chapter 1 where the concept was quietly invoked. In particular, it was tacitly supposed for the mechanical device shown in Fig. 1.3 that the radius R of the wheel and the length L of the hinged rod did not vary with time. These are typical examples of rigid bodies whose motions will be investigated in this chapter. The kinematics of a rigid body in general motion in space will be studied. The main objective will be to learn how the velocity and acceleration of the particles of a rigid body are related to the translational and rotational parts of its motion.