Rotations, Quaternions, and Double Groups (Dover Books on Mathematics)

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.

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" +++

Very clear, and exhaustive and intense book on quaternions and geometry. It's clear and well written.It lacks from an introduction at a good level, so it forces the reader to search for other texts to be read before entering deeply into this. It's impossible to make an all-inside book, but this one uses very important concepts and tools, but leaving them as previous reading.However, very recommended book. One of my best acquisitions covering Geometry issues

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.

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.Dismal.

Fast delivery and as advertised!

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.

Concluante

Ich have purchased this book to help me understand quaternions in view of my bachelors thesis in quantum field theory.At first i didnt like this book, because a lot of the notation is different then i learned it (in germany) and there is way better notation then used in this book. After a while i got accustomed to it and just translated it in a way i would use it.I have now read this book in two weeks and have to say that i learned a lot. It didnt help me much in dealing with quaternionic calculation, but it draws important connections between quaternions and group theory, geometry, important groups like SU(2) and SO(3), clifford algebras, algebraic concepts in general and even topology (homology classes).This definetly helps me in understanding my translation of QFT into quaternions not just from an arithmetic standpoint, but from a much deeper point of view.For only 18€ this is definetly a nice book to get and its also easy to read (good language and also short exercises which can often be made in your head, and if not, they dont leave you with a gap of understanding if you dont do them).