Books about Quaternions from Amazon.com

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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Price: $38.13 [Notify me when price goes down.]

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Price: $11.39 [Notify me when price goes down.]

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: $50.00 [Notify me when price goes down.]

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.

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Price: $29.96 [Notify me when price goes down.]

Mechanics of Flight is a unique combination of theory and applications organized in a logical presentation. It affords readers extensive coverage of individual topics within flight mechanics, including overviews of aerodynamics and propulsion. It also 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..
Price: $89.99 [Notify me when price goes down.]

Illustrated, Including Numerous Examples - Chapters: Definitions And Theorems - Center Of Gravity - Curve Tracing, Tangents - Parallel Projection - Step Projection - Definitions And Theorems Of Rotation - Definitions Of Turn And Arc Steps - Quaternions - Powers And Roots - Representation Of Vectors - Formulas - Equations Of First Degree - Scalar Equations, Plane And Straight Line - Nonions - Linear Homogeneous Strain - Finite And Null Strains - Derived Moduli, Latent Roots - Latent Lines And Planes - Conjugate Nonions - Self-Conjugate Nonions - Etc., Etc..
Price: $14.16 [Notify me when price goes down.]

This volume is produced from digital images from the Cornell University Library Historical Mathematics Monographs collection .
Price: $16.99 [Notify me when price goes down.]

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: $25.00 [Notify me when price goes down.]

The four real division algebras (reals, complexes, quaternions and octonions) are the most obvious signposts to a rich and intricate realm of select and beautiful mathematical structures Using the new tool of adjoint division algebras, with respect to which the division algebras themselves appear in the role of spinor spaces, some of these structures are developed, including parallelizable spheres, exceptional Lie groups, and triality. In the case of triality the use of adjoint octonions greatly simplifies its investigation. Motivating this work, however, is a strong conviction that the design of our physical reality arises from this select mathematical realm. A compelling case for that conviction is presented, a derivation of the standard model of leptons and quarks.
The book will be of particular interest to particle and high energy theorists, and to applied mathematicians.
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Price: $74.95 [Notify me when price goes down.]