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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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Product details
Paperback: 400 pages
Publisher: Princeton University Press (September 8, 2002)
Language: English
ISBN-10: 9780691102986
ISBN-13: 978-0691102986
ASIN: 0691102988
Product Dimensions:
8 x 0.9 x 10 inches
Shipping Weight: 2.1 pounds (View shipping rates and policies)
Average Customer Review:
4.5 out of 5 stars
37 customer reviews
Amazon Best Sellers Rank:
#821,488 in Books (See Top 100 in Books)
This book covers all the info you would want, but the info given is not in normal person terms, and there are like 5-8 chapter questions. Not every one can read something and understand it perfectly, doing problems lets people revers engineer how things work. So if you are like me and learn better through doing problems then reading complicated proofs without a list of variable meanings, then this book might no be for you.
Latitude and longitude look simple enough, at first - just put your finger in the globe, and see which horizontal line crosses which vertical. When you start doing arithmetic, though, things get weird. Measuring longitude in degrees, 179+2=-179. In degrees latitude, 89+2=89, but the longitude changes! And, when you try to figure longitude precisely at the north pole, you run into a singularity. Believe me, you don't want to be in a plane when its navigation programs run into singularities.Those bits of strangeness all vanish when quaternions represent angles. Quaternions are a bit like complex numbers, but with three different complex parts instead of one. They have very nice mathematical properties, even better than rotation matrices, and a compact form.Kuipers gives a clear, thorough introduction to quaternions and their uses in geometric computations. Everything is explained one step at a time, giving the reader plenty of chance to back off and try again when the discussion gets thick. The buildup is very methodical, just about every derivation is carried out in steps that are easy to follow, using legible, standard notation. Kuipers uses side bars to remind the reader about the basics under more complex discussions, keeping an awareness of where a beginner might go off the rails. Since this discusses geometric computations, illustrations are profuse.The book is not for the reader in a hurry. There are lots of gems here, but you really do have to dig through a lot to find them. The illustrations contain all needed information, but it may take some effort to pick them apart. And, like any technical book, this assumes a reader with a certain background. In this case, intuition about 3D objects, trig, and linear algebra are compulsory, but I guess a sufficiently dedicated reader could substitute blind obedience to formulas for linear algebra. Ch.11-13 assumes calculus through partial differentials and ODEs, but many readers can skip these chapters without loss.This is all the how and why of quaterion representations of 3D rotations. It's gently paced, and makes only moderate assumptions about the reader's background. I've never seen this material presently so clearly, from so many angles, anywhere else. Highly recommended.//wiredweird
The great thing about this book is the author goes through detailed expositions of every topic. So if you "get it" the first time, you can skim ahead to the next topic; if not, you can work through the proofs, step-by-step, to make sure you understand it. There's no "the proof is left as an exercise for the interested reader."Another thing I really like about this book is that you don't need to be a mathematician to understand it (i.e. it's perfect for engineers). If there is reference to a mathematical topic, the author defines the terminology and gives you a concise explanation. He will give you enough to make it relevant to the current subject.For example, you don't need to have a grad-school course in groups and fields to be able to understand how they relate to the specific applications of quaternions covered in the book. That cannot be said about some other books on quaternions I have been reading. About all you need here is some knowledge of vectors, matrices and complex numbers.This book is not only tractable but downright accessible. And it is so well organized that, after reading the first few chapters, you may find the specific application of interest to you and jump straight to it.
am already excited. Someone was actually THINKING when they presented the contents AND when they set this book up at the press. It is almost unheard of to have both things happen for a math book. Lots of diagrams, large print, ample room for notes, doesn't start off at a sophisticated level, and doesn't ramp up too quickly.Thought I already knew how to calculate astronomical trajectories from physics and Calculus classes...until I actually tried to do it. Put the plans on hold, ordered this book to help, and went on to other things. There were a half dozen books in line for my reading over the next few months. A minute rummaging through this book after it arrived and it has gone to the head of the reading list.If the logic is as well thought out as the layout, this should be fun!
This book is one of the most understandable and down-to-earth mathematics texts I've ever read. For instance, after presenting a new concept, he'll summarize it again in the sideline of the book every time he refers to it for the next twenty pages or so. At first, I was finding myself getting annoyed, and thinking, "What, does he think I'm stupid?"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!
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