The concept of a rigid body is an artificial one, in that all materials deform when forces are applied to them. Nevertheless, this artifice is very useful when we are concerned with an object whose shape changes little in the course of its motion. In addition, it often is convenient to decompose the motion of a flexible body into rigid-body and deformational contributions.

Most engineering systems feature bodies that are interconnected. Each body must move consistently with the restrictions imposed on it by the other bodies. We refer to these restrictions as constraints. Constraint conditions are the kinematical manifestations of the reaction forces. Indeed, a synonym for reactions is constraint forces. A keystone of analytical dynamics, whose treatment begins in Chapter 7, is the duality of constraint forces and constraint conditions, which enable us to describe one if we know the other. However, in a kinematics analysis one is not concerned with the forces required to attain a specified state of motion.

GENERAL EQUATIONS

When an object is modeled as a rigid body, the distance separating any pair of points in that object is considered to be invariant. This approximation is quite useful because it leads to greatly simplified kinematical and kinetic analyses. Because the distance between points cannot change, any set of coordinate axes xyz that is scribed in the body will maintain its orientation relative to the body.