CHAPTER 6 - MOTION OF A RIGID BODY

Abstract

Publisher Summary A rigid body is defined in mechanics as a system of particles such that the distances between the particles do not vary. This condition can be satisfied only approximately by systems that actually exist in nature. The majority of solid bodies, however, change so little in shape and size under ordinary conditions that these changes may be entirely neglected in considering the laws of motion of the body as a whole. There are two systems of coordinates: a fixed system, that is, inertial, system XYZ, and a moving system x1 = x, x2 = y, x3= z, which is supposed to be rigidly fixed in the body and to participate in its motion. The origin of the moving system may conveniently be taken to coincide with the centre of mass of the body. The position of the body with respect to the fixed system of coordinates is completely determined if the position of the moving system is specified. An arbitrary infinitesimal displacement of a rigid body can be represented as the sum of two parts. One of these is an infinitesimal translation of the body, whereby the centre of mass moves to its final position but the orientation of the axes of the moving system of coordinates is unchanged. The other is an infinitesimal rotation about the centre of mass, whereby the remainder of the body moves to its final position. The chapter further discusses the angular momentum of a rigid body, rigid bodies in contact, and motion in a noninertial frame of reference.