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

Format:

Book

Author/Creator:

Kuipers, J. B., Author.

Language:

English

Subjects (All):

Quaternions.

Physical Description:

1 online resource (xxii, 371 pages) : illustrations

Place of Publication:

Princeton, NJ : Princeton University Press, [2020]

Language Note:

In English.

Summary:

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:

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

Notes:

Includes bibliographical references (pages 365-366) and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 05. Mai 2020)

ISBN:

9780691211701

0691211701

OCLC:

1153561813