This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

The major objective of the ideas presented in this paper is to enable instructors to give their students a better understanding of linear transformations in three dimensions based upon the maneuvering concepts of pitch, roll, and yaw. These terms are commonly used in maneuvering aircraft and submarines, so that it is easy to make use of physical models to illustrate these transformations.

The three basic transformations which provide the ability to maneuver are rotations. In this paper, we denote them by
P_psi which pitches the nose down through the angle psi,
R_phi which rolls the left wing up through the angle phi,
and
Y_theta which yaws the nose toward the left wing through the angle theta.

By using pictures and physical models, we illustrate these rotational transformations. We also demonstrate inverses and compositions of transformations, as well as related properties. We conclude with a collection of exercises, some making use of physical models, and some which are computational in nature. Several of these are appropriate for group activities and projects.

David W. Boyd, Valdosta State University
Richard H. Elderkin, Pomona College