Rating: 
Summary: Clearly written and extremely useful.
Review: >Professor Kuipers, > >I wanted to drop you an email and thank you for authoring your marvelous >book on Quaternions. > >It is clearly written and extremely useful which seems to be a violation of >the laws of most works in mathematics. > >Les > >---------------
Rating:
Summary: Helpful
Review: An excellent book if one is to commence on learning the intricacies of rotation sequences. For those in the aerospace industry, specifically those who work in the field of stability and control/attitude control may find this book quite conducive to their craft.
The author begins with summarizing basic algebra to matrix methods and begins his ascent into the world of coordinate transformations.
As those who work with transformations know, it can be cumbersome to visualize what may be happening when a vector is transformed into one rotation frame to another. However the book enlightens us with showing the fundamentals behind a fixed vector (coordinate frame rotate) and fixed coordinate system (vector rotates) and shows us how much of a difference there is in actual coordinates of the resulting transformation.
The fundamentals are definitley here folks. If you are just starting out to learn about the ambiguous structure of quaternions and rotations, or need to refresh your memory, this book is ideal.
All derivations are laid out so that an undergrad can understand it, but so that an industry professional can also use it as a reference. I highly recommend.
Rating:
Summary: Clear and very readable
Review: As a "primer", this book is right on target. The theory presentation is truly legible, with remarkable notes on each page, just collateral to the main text, fixing notions or fulfilling the contents with concise demonstrations.The first chapters are a fast, but complete review of algebraic basics, good for an expert and a solid start for a novice (albeit it is instrumental to the succesive pages, refer to other specific books for consolidating your preparation). Then the volume start to unleash the true topics, showing the mathematical properties of quaternions, as a rotation operator and related geometry, to end up in a well suited exposition of spherical geometry, calculus and pertubation theory (linked to dynamics and kinematics fields).
Quite pleasant to discover is the applications section, especially computer graphics, while its airspace use is just introduced. Nevertheless, the author has neatly achieved his goal.
Rating:
Summary: Step by step
Review: As an engineer assigned to find a way to use quaternions to solve a real time orientaion tracking problem I found this book more than useful, it has been a complete reference. I recommend this book to anyone who needs to understand and use quaternions now. A practical, clear and thorough presentation, Thank you Dr. Kuipers !
Rating:
Summary: Step by step
Review: As an engineer asssigned to find a way to use quaternion methods to solve a real time orientation tracking problem I have found Dr. Kuipers book to be a complete reference. I recommend this book to anyone who needs to understand and use quaternions now. Thank you Dr.Kuipers.
Rating:
Summary: First book I've seen that really presents them clearly ...
Review: I have struggled with the concept of quaternions for a while. Being involved in the flight simulation industry, I finally found myself needing to know much more about them and understanding them thoroughly. This book presents the subject matter from the start in an easily understandable progression. Various practical examples are also given which make this book the definitive source for quaternion understanding.
Rating:
Summary: I am the Quaternion Book's Author
Review: I merely want to share with you an excellent review of my Quaternion Book. The review appeared in the Nov/Dec'03 issue of Contemporary Physics, vol6., and was written by Dr Peter Rowlands, Waterloo University, UK. The review is herewith attached (if I may) otherwise I'll paste the text). It's probably too long --- but you now know where to find it. Here goes: The following Book Review Appeared in Journal: Contemporary Physics},
Nov/Dec 2003,
vol 44, no. 6, pages 536 - 537 · · ·
Quaternions & Rotation Sequences
A Primer with Applications to Orbits, Aerospace, and Virtual Reality
by JACK B. KUIPERS
Princeton University Press. 2002, £24.95(pbk), pp. xxii +
371, ISBN 0 691 10298 8.
Scope: Text.
Level: Postgraduate and Specialist. } Quaternions are one of the simplest and most powerful
tools ever offered to the physicist or engineer. Unfortunately,
they are relatively little known because a centuryold
prejudice (the result of a family feud involving vector
theory) has been responsible for keeping them out of
university courses. The fact that quaternions have never
really found their true role has become a self-fulfilling
prophecy, despite their reappearance in various disguised
forms such as Pauli matrices, 4-vectors, and, in a complex
double form, in the Dirac gamma algebra. The straightforward
manipulation of this relatively simple formalism,
however, means that, to a quaternionist, such things as Minkowski space-time and fermionic spin are no longer
mysterious unexplained physical concepts but merely
inevitable consequences of the fundamental algebraic
structure, while even ordinary vector algebra as David
Hestenes has shown (Space-Time Algebras, Gordon and
Breach, 1966) is much better understood in terms of its
quaternionic base. The immense value of the quaternion
algebra is that its products are ordinary algebraic products,
not the dot or cross products of standard vector algebra,
although they also include these concepts.
Despite many statements to the contrary, quaternions
are by no means short of serious applications, either. Often
in highly practical contexts, and, in every application that I
know of, where a quaternion formulation is possible, this
formulation is invariably superior to any more 'conventional'
alternative. Kuipers, in his splendid book, effectively
shows this in the eminently practical case of the aerospace sequence and great circle navigation by demonstrating how
the same calculations are done, first by conventional matrix
methods, and then by quaternions. Rather than abstractly
defining quaternion algebra and then seeking possible
applications, he prepares the ground well by describing
the application first, and then developing the quaternion
methods which will solve it. It is not until chapter 5, in fact,
that quaternion algebra is seriously introduced. However,
Kuipers sets this on a
firm basis by establishing early on the connection with
complex numbers, matrices and rotations. These subjects
are discussed with great thoroughness in the early chapters.
The work is avowedly a primer, and so nothing is taken for
granted. The student can begin at the beginning and follow
the argument through stage by stage, with virtually no
prior knowledge of the subject. The real core of the
mathematical analysis comes in chapters 5 to 7, with solid
and relatively easy to follow treatments of quaternion
algebra and quaternion geometry, together with an algorithm
summary, relating quaternions to such things as
direction cosines, Euler angles and rotation operators. The
superiority of quaternion over, for example, matrix
methods is demonstrated by Kuipers' statement on p. 153
that the quaternion rotation operator (unlike the matrix
one) is 'singularity-free'. Following the main application to
the aerospace sequence and great circle navigation, there
are further chapters on spherical trigonometry, quaternion
calculus for kinematics and dynamics, and rotations in
phase space, with two final chapters devoted to applications
in electrical engineering (dipole radiation signals sent by a
source to a sensor, and then correlated using a processor)
and computer graphics.
The final application is especially interesting as quaternions
have been behind much of the rapid development of
computer graphics. One role that quaternions have always
fulfilled is their applicability to 3-dimensional structures,
and the otherwise difficult problem of rotation, especially
when time-sequencing is involved. Computer software
engineers have exploited this while physicists have missed
out. The creation of a 'natural' 3-dimensionality, using the
'vector' or imaginary part of quaternions was, of course,
the original reason for their creation; but, while the
remaining 'scalar' or real part was originally thought of
as a problem by the proponents of vector theory, it is now
seen as a bonus, allowing the incorporation of time as a
natural result of the algebra. We cannot escape the fact that
we live in time within a 3-dimensional spatial world, and
quaternion algebra appears to be the easiest way of
comprehending and manipulating this 3-or 4-dimension-
ality. Kuipers shows us examples of the exploitation of the
technique in aerodynamics, electrical engineering and
computer software design, but it also has relevance in
topology, quantum mechanics, and particle physics.
It is frankly as absurd for physicists and engineers to
neglect quaternions as it would be for them to disregard
complex numbers or the minus sign. It is important that
students get to learn about this spectacularly simple and
powerful technique as early as possible, and Kuipers has
provided us with the perfect opportunity of remedying a
massive defect in our technical education. His book has everything that 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.
DR PETER ROWLANDS
(University of Liverpool)
Rating: 
Summary: A word of caution
Review: I was very disappointed when I started reading the book and immediately noticed a number of errors in the formulae. These were most likely typos but still can be confusing at times. As the other reviewers mentioned, the book has a very interesting, and in my opinion very good, teaching sytle, but don't take all the formulae by heart if you are going to use it as a reference book. (PS. My comments are on the first print of the book, I hope the errors have been corrected in the later prints.)
Rating: 
Summary: A good introduction to quaternions
Review: Is it possible to recommend a book and still say that it needs revision? It needs revision precisely because it is a good book and may well find more readers. The book does what no other does as far as I know; it introduces quaternions in elementary terms and shows some, at least, of how useful the concept is. The topic is neglected in textbooks for students at this level and probably even more generally. And yet I do think that the author could revise this book substantially and produce a better one.
Rating:
Summary: An oustanding work on rotations for the practitioner
Review: My graduate school work was in theoretical quantum mechanics, and was especially concentrated in the group properties of rotations. I can honestly say that I would have been twice as effective if I had this reference available then. Kuiper does an outstanding job of pulling together the traditional matrix-based approach to describing rotations with the less-frequently encountered quaternion approach. In doing so, he clearly shows the benefits of the quaternion algebra, especially for computer systems modeling rigid body rotations and virtual worlds. The exposition is clear, concise, and aimed at the practitioner rather than the theoretician. The examples are taken from classical engineering problems -- a refreshing change from the quantum-mechanical problems I was used to from previous works on the subject. Despite the practical foocus, though, there is plenty of material here for those more interested in understanding the minutia of the SO(3) symmetry group. And unlike most work in this field, he doesn't stop with algebra, but includes the calculus of rotation matrices and quaternions using material on kinematics and dynamics of rigid bodies, celestial mechanics, and rotating reference frames. I give the book my highest recommendation. It should be considered an essential reference work for anyone who encounters rotational problems with any frequency. --Tony Valle
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