"Many of the concepts of three-dimensional kinematics of rigid bodies were introduced in Chapter 5, but only solutions of dynamics problems for plane motion-that is, motion with just three degrees of freedom-were presented in Chapters 6 and 7. Although many motions can be modeled two dimensionally, complex machines, airplanes, automobiles, the human body, and, in fact, most things move in a three-dimensional manner. The major difficulty in extending our study to three dimensions is that we will now have six degrees of freedom. The three translational degrees of freedom were considered in Chapters 1 and 2 when we studied particle dynamics; now we need to examine the three rotational degrees of freedom." p524

COORDINATE TRANSFORMATIONS
EQUATIONS THAT ARE USED TO CHANGE FROM ONE SYSTEM OF COORDINATES (MEASUREMENTS) TO ANOTHER.

EQUATION
A MATHEMATICAL EQUALITY RELATING PARAMETERS OR MEASUREMENTS

EULER EQUATIONS OF MOTION
A SET OF THREE DIFFERENTIAL EQUATIONS EXPRESSING RELATIONS BETWEEN FORCES, MOMENTS, VELOCITIES AND ACCELERATIONS OF A ROTATING, RIGID OBJECT.

INFINITESMAL
A VERY SMALL BIT OR AMOUNT

INFINITESMAL ROTATION
A VERY SMALL ROTATION OF AN OBJECT THROUGH A TINY ANGLE.

ROTATION
MOTION OF ALL PARTS OF A BODY IN CIRCLES AROUND AN AXIS.