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[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
Product Description
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.
Mathematics, as with most subjects in science and engineering, has a long and varied history. Read the first page
Concordance
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
Then I considered the alternative, the terse style of so many mathematical texts that has me regularly flipping between eight different pages trying to put everything together. I stopped complaining and started appreciating Kuipers' approach.
Kuipers does assume a certain amount of familiarity with mathematics, but not any knowledge in particular, as he reviews basic matrix multiplication and the like at the beginning of the book.
For a topic that can seem daunting (our artist always makes fun of me using seemingly gratuitous big phrases like "spherically interpolated quaternion splines") this book makes it very understandable. If you need to work with computational rotation, for a flight sim, robotics visualization, or (most importantly) for a computer game, I can't recommend this book highly enough!
An exceptional introduction in which the complex plane is introduced in perhaps one of the most cleanest descriptions of the theory I have seen. The later chapters build on this, and it all comes together quite nicely.
Whatever application you decide to use the text for, chances are it covers it in some way. A very good book, and highly recommended.
I recommend it to anyone who wishes to understand Quarternions.
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