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Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality
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..
Price: $37.05
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Rotations, Quaternions, and Double Groups
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On Quaternions and Octonions
An investigation of the geometry of quaternion and octonion algebras, this book is intended for mathematicians, physicists, and crystallographers at any level--from undergraduate to professional--who are interested in the symmetries of low-dimensional space. The book can also be used as a text for graduate courses in many mathematical fields, including geometry, group theory, algebra, and number theory. A Selection of Topics Covered:
The geometry of complex numbers
Quaternions and 3-dimensional groups
Quaternions and 4-dimensional groups
The Hurwitz integral quaternions
Moufang loops
Octonions and 8-dimensional geometry
Integral octonions
The octonion projective plane.
Price: $28.82
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Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available. The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important-a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions. * Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing. * Covers both non-mathematical and mathematical approaches to quaternions. * Companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities..
Price: $51.95
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Mechanics of Flight
Complete and accessible coverage of flight mechanics Mechanics of Flight is a unique combination of theory and applications organized in a logical presentation. This book provides extensive coverage of individual topics within flight mechanics, including overviews of aerodynamics and propulsion. This complete instructional reference offers a full range of modern and classical techniques for applying fundamental principles to the solution of engineering problems in fight mechanics. Mechanics of Flight explores the basic principles of flight mechanics with the help of many worked examples, starting with simple problems involving steady-level flight and building to more complex ones such as the analysis of turning flight and spins. Special coverage found here--and not in most books on the subject--includes a detailed presentation of the quaternion formulation for six-degree-of-freedom flight simulation, including treatment of efficient numerical integration methods. Students and practicing engineers who are familiar with the principles of static stability and control can begin the study of flight dynamics in Chapter 7, starting with a review of coordinate systems and notation as well as a development of the more general rigid-body equations of motion. Mechanics of Flight is an essential volume for mechanical and aerospace engineering students and a valuable reference for practicing engineers in the aerospace industry..
Price: $84.99
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Introduction to Quaternions: With Numerous Examples
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Quaternions, Clifford Algebras and Relativistic Physics
The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus. .
Price: $33.07
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Vector analysis and quaternions
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