Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality

by J. B. Kuipers

Princeton University Press | September 8, 2002 | Trade Paperback

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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.

Format: Trade Paperback

Dimensions: 400 pages, 10 × 7 × 0.98 in

Published: September 8, 2002

Publisher: Princeton University Press

Language: English

The following ISBNs are associated with this title:

ISBN - 10: 0691102988

ISBN - 13: 9780691102986

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– More About This Product –

Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality

by J. B. Kuipers

Format: Trade Paperback

Dimensions: 400 pages, 10 × 7 × 0.98 in

Published: September 8, 2002

Publisher: Princeton University Press

Language: English

The following ISBNs are associated with this title:

ISBN - 10: 0691102988

ISBN - 13: 9780691102986

About the Book

"This is the most complete discussion of quaternions and their applications that I have seen."--Alan C. Tribble, author of "A Tribble's Guide to Space"

Table of Contents

List of Figures
About This Book
Acknowledgements
1 Historical Matters 3
2 Algebraic Preliminaries 13
3 Rotations in 3-space 45
4 Rotation Sequences in R[superscript 3] 77
5 Quaternion Algebra 103
6 Quaternion Geometry 141
7 Algorithm Summary 155
8 Quaternion Factors 177
9 More Quaternion Applications 205
10 Spherical Trigonometry 235
11 Quaternion Calculus for Kinematics and Dynamics 257
12 Rotations in Phase Space 277
13 A Quaternion Process 303
14 Computer Graphics 333
Further Reading and References 365
Index 367

From the Publisher

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.

From the Jacket

"The text is written in a clear and readable style well suited for students wishing to master fundamental quaternion concepts."--Mark C. Allman, Senior Engineer, The Boeing Company

"This is the most complete discussion of quaternions and their applications that I have seen."--Alan C. Tribble, author of A Tribble''s Guide to Space

Editorial Reviews

"[A] splendid book . . . everything one could wish for in a primer. It is also beautifully set out with an attractive layout, clear diagrams, and wide margins with explanatory notes where appropriate. It must be strongly recommended to all students of physics, engineering or computer science."--Peter Rowlands, Contemporary Physics
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