Synopses & Reviews
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.
Review
"[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
Review
"This book will appeal to anyone with an interest in three-dimensional geometry. It is a competent and comprehensive survey. . . . This book is unique in that it is probably the only modern book to treat quaternions seriously. . . . A valuable asset."--Aeronautical Journal
Review
This book will appeal to anyone with an interest in three-dimensional geometry. It is a competent and comprehensive survey. . . . This book is unique in that it is probably the only modern book to treat quaternions seriously. . . . A valuable asset. Aeronautical Journal
Review
[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
Synopsis
"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"
Synopsis
Includes bibliographical references (p. 365-366) and index.
Synopsis
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.
Synopsis
"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
Synopsis
"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
Synopsis
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.
Synopsis
"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
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 |