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Customer reviews

3.7 out of 5 stars
Rotations, Quaternions, and Double Groups (Dover Books on Mathematics)
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on March 28, 2014
Quaternions are an extremely arcane and difficult area to study. There are over a half dozen books in print covering the subject and getting a decent look at them without paying a hundred dollars is a small feat in itself. Altman's book does the job well without being long winded. It gives a thorough historical introduction and proceeds into the material at a comfortable pace while providing sufficient diagrams to keep the subject clear. At about 277 pages, it should provide several weeks of unraveling the puzzle before the reader manages to encompass the entire subject.

Quaternions supply the solution to avoiding "gimbal lock" when your rotational computation takes your Euler analysis into alligning two of your three rotational axies into the same plane. This effect makes your craft or creature rotation lockup during simulation and has caused more than one remotely piloted vehicle to crash. Avoid the embarrassment and avoid the whole problem by using Quaternions instead.

Unless you are an aeronautical engineer, you are probably looking into this book to support a computer game or are applying a factory furnace simulation for energetic particle flux in a chemical reactor or combustion engine. This material will support such activities well. You will probably need a serious GPU to serve up the vectorization on a half million molecules in those cases. You can use these equations to support kinematic simulations for electrodynamic forces in electric motors and propulsion systems. Just remember that electron spin is a quantum concept, the electrons don't actually have a rotational momentum as a top does.

If you need more graphic detailing to understand the subject, I recommend "Visualizing Quaternions", which has better graphics along with a heftier price. And in either case, you need to be comfortable with vector mathematics and matrix operations to avoid getting stuck in the middle of this material. Have a great time powering your simulations with this mathematical tool.
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on December 4, 2016
This book is awesome! If you want a rigorous rundown of all the generators you run across in quantum mechanics, their eigenfunctions, and a nice first stab at spinors while getting the historical context, then snag this book. I will say that I lost steam during the spinor representations chapter, but everything before that I read in a little over a week. Just couldn't put it down.
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VINE VOICEon April 8, 2010
This work is as fluid, clear and sharp as can be on this general subject area -- rotations, quaternions and double groups -- and the related Clifford algebra, linear algebra, linear transformations, bilinear transformations, tensors, spinors, matrices, vectors and complex numbers -- and in relation to quantum physics and its spin-offs. "Rotations, Quaternions and Double Groups" surveys ALL those topics and more in a fluid, clear and sharp way. In addition, the careful geometric AND algebraic presentation thru-out this fine primer by Simon Altmann is an exemplar of mathematical presentation immediately favoring application via such methods as the very useful Dirac Bra-Ket notation.

The nearly forgotten Rodrigues rotation-angles are overlooked in most works besides this one and a few others -- yet are indeed the best approach to geometric / physical rotations -- via exact matching of geometric notation with geometric rotation -- unlike any other approach. Rodrigues rotation-angles MAP EXACTLY to actual rotations unlike any other method to fine tune quaternionic rotations -- removing all ambiguity and imprecision. The difference being seen in all areas -- including math, physics and rotation computation. Quoting from the introduction -- "Moreover, if all the rotations are parametrized by Rodrigues's quaternions, then all matrices and phase factors are uniquely and precisely determined. No trial and error is required and thus the method is ideally suited to calculation by computer" +++
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on July 31, 2016
Like others, I found this book to be incredibly disappointing. His approach to explaining even the simplest of mathematical concepts is locked within a dated, obscure, and ineffective approach to teaching the subject. It reads as if the author wished to make such a rich and interesting subject as boring and cryptographic as possible. Richard Feynman would weep after reading the first chapter of this travesty.
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on October 26, 2007
This book will be difficult for "paper mathematicians" because it describes concepts of orientations in multidimensional configuration space that requires visual / spatial ability. It does so with with a depth and granularity that can be appreciated by those who work with these "tools". This small book is not a quick read, nor a general overview. It takes time to ruminate on these words to gain understanding of increasingly important behaviors in classical and quantum physics, as well as modeling the complexity in systems. But, these rewards require an investment of time and thought.
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on May 15, 2006
This book has the best explanation of Clifford algebra

that I've ever seen.

The coverage of dihedral, space groups, quaternions and even projective

diagrams is just very ,very good.

He introduces "The Rodrigues programme" which is

a very good angular approach to quaternions

that actually predates Hamilton's quaternions

but has been overlooked.

He doesn't spare on word definitions and explanations.

The index is fully operational

and definitions are for the most part complete and understandable.

In other words he actually doesn't just pretend to teach

group theory, he actually does!

If you have always wondered about SU(2) and quaternions, this is the book

that you "need" to read.

Roger L. Bagula
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on June 30, 2007
This book displays great erudition. The reference section lists 140 books or articles about quaternions and rotations, going back to the 19th and even 18th centuries. The author shows off his command of this literature, taking a very thorough approach, bringing up subtle points that experts on the subject might not have fully grasped. Unfortunately, for a non-expert like me, the result is often bafflement.

Some passages just seem obscure, for example on p 28 "rotations are an accident of three dimensional space. In spaces of any other dimensions the fundamental operations are reflections". There is no further discussion of this point, which is far from obvious to me.

My background is in computing. I was looking for a general introduction to quaternions and their applications. This book did not meet my objectives. It is inexpensive and well produced but the contents too inaccessible.
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on October 29, 2016
Fast delivery and as advertised!
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on May 8, 2007
I came to this book with a good understanding of matrices, tensors, complex numbers, quaternions and some quantum mechanics. But I was unsure about spinors, and I hoped this book would help. It didn't.

Much time is wasted is confusing and unnecessary quibbles. Each rotation can be represented by either of two quaternions. But which one? Far too much is made of this dilemma. Each rotation has two poles. Far too much is made of this too.

The author's plan seems to be to create as much confusion as possible, and then show how quaternions can clean it all up, like a superhero at the end of a movie. Much better to *start* with quaternions and never let the confusion arise in the first place.

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