Quaternions and Rotation Sequences : : A Primer with Applications to Orbits, Aerospace and Virtual Reality / / J. B. Kuipers.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
• VerfasserIn: Kuipers, J. B.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2020]; ©1999
• Year of Publication: 2020
• Language: English
• Physical Description: 1 online resource (400 p.) :; 121 figures

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.

Table of Contents

Frontmatter -- Contents -- List of Figures -- About This Book -- Acknowledgements -- Chapter 1. Historical Matters -- Chapter 2. Algebraic Preliminaries -- Chapter 3. Rotations in 3-space -- Chapter 4. Rotation Sequences in R3 -- Chapter 5. Quaternion Algebra -- Chapter 6. Quaternion Geometry -- Chapter 7. Algorithm Summary -- Chapter 8. Quaternion Factors -- Chapter 9. More Quaternion Applications -- Chapter 10. Spherical Trigonometry -- Chapter 11. Quaternion Calculus for Kinematics and Dynamics -- Chapter 12. Rotations in Phase Space -- Chapter 13. A Quaternion Process -- Chapter 14. Computer Graphics -- Further Reading and Some Personal References -- Index