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Title: Quaternions and Rotation Sequences : A Primer with Applications to Orbits, Aerospace and Virtual Reality by J. B. Kuipers ISBN: 0-691-10298-8 Publisher: Princeton Univ Pr Pub. Date: 19 August, 2002 Format: Paperback Volumes: 1 List Price(USD): $35.00 |
Average Customer Rating: 4.72 (18 reviews)
Rating: 4
Summary: An easy to follow primer lacking references
Comment: The main asset of this delightful book is its methodical and unencumbered presentation of the most basic mathematics, vector and matrix operations from the first page. Specifically, it illustrates basic algebraic field theory and generalizes complex numbers into quaternions in an uncomplicated way. The fluid presentation encourages the reader to continue through the necessarily lengthy introduction of the classical rotation operators (as detailed use of quaternions doesn't start until about 100 pages, in Chapter 5).
I appreciated the fact its introductory nature is honestly clarified by the subtitle: it is a self-declared primer. It is also one of the few textbooks I have seen making extensive use of a marginal gloss (explanatory notes in the margin), which seems much more efficient than footnotes or appendices. Many facts are repeated - noticeable but not too annoying, and handled well in the gloss. This level of presentation will certainly benefit most readers new to the subject. Anyone writing a technically oriented textbook should consider reviewing this title for its format alone.
The book defines a quaternion as a 3-D vector plus a scalar. Defining the quaternion with these more conventional mathematical notions makes the very concept more approachable. But it is not clear whether this (and other) notation is truly unique to this book or otherwise widely acknowledged in literature. For example, most of the notation adopted for classic rotation operators seemed unnecessarily different (and therefore slightly confusing) compared to those few other engineering and science textbooks I've been able to reference on the subject. And a few terms, such as "kyperplane", appear unique to this book alone.
Considering that this is an introductory textbook, the recommended "further reading" list was by far the most disappointing aspect of this title. Out of sixteen (16) meager references provided, 1/4 are Prof. Kuipers' own patent declarations; the rest are mostly hard-to-get Air Force reports, out of print books, and a few specialty journal articles. The lack of specific references is especially bothersome when facts or theorems are cited without support or proof, such as "Euler's Theorem" (p. 83).
Engineers and engineering students should also be aware that some of the "applications to orbits and aerospace" (from the subtitle) appear to be more for academic or illustrative purposes than for immediate, practical application. For example, the publisher's on-line table of contents identifies "Chapter 11 - Quaternion Calculus for Kinematics and Dynamics." However, this chapter doesn't really cover the conventional transformations of relative velocity or accelerations with respect to rotating frames of reference, which is essential to the study of dynamics and kinematics of air and space vehicles. In the preface, the author acknowledges that "It was difficult knowing where to stop, since the subject deserves much more attention and greater depth." As a result, the book may have slightly more appeal to those interested in 3-D programming and visualization.
God bless the author, who at age 80 apparently supplied the textbook copy in camera ready form. Unfortunately, my 3rd printing still contains many obvious typographical errors, which is the publisher's responsibility (who holds the copyright). A lack of editorial review normally implies that less obvious errors are lurking in those all-important equations, but thankfully Prof. Kuipers is kind enough to provide an errata sheet if the reader requests it via email. However, the reader should be aware that his printed book is still be published uncorrected, and no official errata appears at the publisher's website at this time.
In summary, I would recommend this primer for the engineering student or programmer with a novice to intermediate level of familiarity with rotational sequences. The book's style of presentation is commendable, and the extensive gloss makes the subject matter more understandable to the beginner. Discussions of some engineering applications, as well as specific topics such as orbital mechanics, gravitational theory, etc., are presented with far less detail, clarity, and rigor. While disappointing, this is forgivable as the author seemingly intends to illustrate, rather than develop rigorously complete relationships, for these applications. However, the lack of modern, easily obtained references and some seemingly unique notation may give this title less longevity as a research or reference text.
Rating: 5
Summary: I am the Quaternion Book's Author
Comment: 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: 4
Summary: A good introduction to quaternions
Comment: 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.
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