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

Paperback | September 8, 2002

byJ. B. Kuipers

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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.

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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 geome...

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

Format:PaperbackDimensions:400 pages, 10 × 7 × 0.98 inPublished:September 8, 2002Publisher:Princeton University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0691102988

ISBN - 13:9780691102986

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Extra Content

Table of Contents

List of Figures
About This Book
Acknowledgements
1Historical Matters3
2Algebraic Preliminaries13
3Rotations in 3-space45
4Rotation Sequences in R[superscript 3]77
5Quaternion Algebra103
6Quaternion Geometry141
7Algorithm Summary155
8Quaternion Factors177
9More Quaternion Applications205
10Spherical Trigonometry235
11Quaternion Calculus for Kinematics and Dynamics257
12Rotations in Phase Space277
13A Quaternion Process303
14Computer Graphics333
Further Reading and References365
Index367

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