Quaternions and Rotation Sequences

A Primer with Applications to Orbits, Aerospace and Virtual Reality

Jack B. Kuipers

394 pages, parution le 09/12/2002

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Résumé

Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.

The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.

Contents

Historical Matters
Algebraic Preliminaries
Rotations in 3-space
Rotation Sequences in R3
Quaternion Algebra
Quaternion Geometry
Algorithm Summary
Quaternion Factors
More Quaternion Applications
Spherical Trigonometry
Quaternion Calculus for Kinematics and Dynamics
Rotations in Phase Space
A Quaternion Process
Computer Graphics

L'auteur - Jack B. Kuipers

Jack B. Kuipers is Professor Emeritus of Mathematics at Calvin College. In addition to publishing papers and research notes on quaternions, he spent seventeen years in the aerospace industry where his work included developing applications of quaternion theory for aerospace systems. He also developed a six-dimensional graphics system and, as a consequence, is regarded by some as the founder of virtual reality.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Princeton University Press
Auteur(s)	Jack B. Kuipers
Parution	09/12/2002
Nb. de pages	394
Format	19 x 25,4
Couverture	Broché
Poids	896g
Intérieur	Noir et Blanc
EAN13	9780691102986
ISBN13	978-0-691-10298-6