About This Book
This book is intended for all the mathematicians, engineers, and physicists who have to know, or who want to know, more about the modern theory of quaternions. Primarily, as the title page suggests, it is an exposition of the quaternion and its primary application in a rotation operator. In a parallel fashion, however, the conventional or more familiar matrix rotation operator is also presented. This parallel presentation affords the reader the opportunity for making comparative judgments about which approach is preferable, for very specific applications.
This book readily divides into three major areas of concern:
The first three or four chapters present introductory material which establishes terminology and notation to be used later on.
The mathematical properties of quaternions are then presented, including quaternion algebra and geometry. This is followed by more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in certain situations involving dynamics and kinematics.
Lastly, state-of-the-art applications are discussed. A six degree-of-freedom electromagnetic position and orientation transducer is presented. With this we end with a discussion of computer graphics, necessary for the development of applications in Virtual Reality.
The writing of this book was early-on supported by the United States Air Force, whose objective was to provide a primer on quaternions, suitable for self-study. Our primary concern was that the book be written at a level such that much of the subject matter would be accessible to those with a modest background in mathematics. With this in mind, the quaternion is defined and its algebra is introduced and developed. Several applications of the quaternion, the quaternion rotation operator, and quaternion rotation sequences are presented. A preview of the Table of Contents will provide the reader with a measure of the intent and scope of this book.