Finite Rigid Body Displacements

Our study of rigid body motion thus far has focused mainly on equations (2.27) and (2.30) for the velocity and acceleration of a body particle. Although they actually represent nothing more than the application of the defining equations (1.8) and (1.9) to the special class of rigid body motions, these rudimentary equations were found to be especially useful because they separate and exhibit clearly the translational and rotational parts of the body’s motion in space, and the terms have simple geometrical and physical interpretations. We have seen in several examples that a major advantage of these relations is that the usual differentiation operations have been replaced almost entirely by simple vector algebraic operations. Moreover, as shown in Examples 2.3 and 2.4, equations (2.27) and (2.30) also may be used to obtain information when only the values of the vectors at a particular instant of time and not the vector functions themselves are given in a problem. We shall see in the next chapter that these basic equations play a particularly important role in the description of motion referred to a moving reference frame.