Physics Today Review
by
Meinhard E. Mayer
University of California, Irvine
May 1999
Classical mechanics
has for years been the Cinderella of the graduate curriculum in
many physics departments. Some departments have actually stopped
teaching it. Recently, mainly as a result of the renewed interest
in deterministic chaos (and the discovery that the warhorse of mechanics-the
Solar System-falls into this category), there has been renewed interest
in the subject, and the number of modern textbooks on classical
mechanics is increasing. Many of these, however, require a familiarity
with differential geometry, which has led to some reluctance to
adopt them in many graduate schools. Classical Dynamics, by Jorge
V Jos6 and Eugene J. Saletan, should certainly redress this: It
strikes the right balance between physical reasoning and mathematical
sophistication, at the same time as it takes the reader to the forefront
of active research in the field.
From the focus of the book, one
can guess that the authors' backgrounds are in particle or plasma
physics rather than celestial mechanics. Jos6 is the Matthews
Distinguished University Professor and director of the Center
for Interdisciplinary Research on Complex Systems at Northeastern
University. Saletan, a professor emeritus of physics at Northeastern,
is coauthor with Alan Cromer of Theoretical Mechanics (Wiley,
1971) and with Giuseppe Marmo, Alberto Simoni, and Bruno Vitale
of Dynamical Systems (Wiley, 1985).
Classical Dynamics, a rather
hefty book, can be used as a textbook and as a reference on newer
topics in mechanics. It does not confine itself to particle mechanics,
and it contains an interesting chapter on continuum mechanics
and nonlinear field theory. It introduces the reader along the
way to some of the differential geometric aspects of Lagrangian
and Hamiltonian mechanics, without getting too involved in the
mathematical nitty-gritty. It contains a wealth of worked examples
and interesting problems, the solutions to which are available
(to instructors) on DOS or Macintosh diskettes in PDF format.
Some of the book's refreshing
features bear mentioning. Instead of the usual presentation, starting
from Newton's laws or Hamilton's principle, Newton's laws are
"derived" (in the spirit of Ernst Mach) by analyzing momentum
conservation in two-particle interactions in an inertial frame.
Mass thus appears naturally via mass ratios, and force is treated
as it should be, as acceleration. The notions of stability and
chaos appear as early as page 10.
The book moves on briskly to
the Lagrangian treatment of constrained problems, and the notions
of manifold and tangent bundle appear in chapter 2, with lots
of good illustrations to facilitate understanding. Motion of charged
particles in electromagnetic fields is used to illustrate gauge
invariance.
The chapter on variational principles
is succinct but discusses such difficult topics as nonholonomic
constraints and dissipation with much greater clarity than do
most textbooks I know. The chapter ends with a discussion of Noether's
theorem and active and passive symmetry transformations.
There is a nice chapter on classical
and inverse scattering, including chaotic scattering (with an
easy introduction to fractal dimensions). A useful application
is the scattering of a charge by a magnetic dipole (the St6rrner
problem). The chapters on Hamiltonian dynamics, canonical transformations,
and completely integrable systems are clear and easy to read.
The Kolmogorov- Amold-Moser (KAM) theory is clearly explained,
based on a presentation of Jean Behssard and preceded by good
examples of deterministic chaos. The necessary number-theoretic
concepts are explained in an appendix.
Recent interesting developments,
such as the Hannay angle, are also introduced. A brief chapter
on the rigid body is followed by a nice chapter on continuum theories,
nonlinear field theories, and solitons. Starting with the Sine-Gordon
equation as the continuum limit of a chain of coupled pendulums,
the authors introduce the reader to Maxwell's equations, some
special relativity, solitons, and the Euler and Navier-Stokes
equations.
The book is nicely typeset and
printed on an ivory-colored, heavy-textured paper that is pleasant
to the sight and touch, and the illustrations are very good. There
are few if any obvious mistakes and surprisingly few mis-prints
(most of them in proper names). I highly recommend this book to
instructors and students alike.
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Amazon.com Reader Review
by
George Hrabovsky
Madison, Wisconsin, USA
February 11, 1999
This book combines the standard topics
covered in a Goldstein-type course; but in a fresh light. Using
techniques of modern geometry, presented in an understandable way,
it explores not just the solutions of dynamical equations, but the
behavior of those solutions over the manifold in which they operate.
The book begins by applying this geometry to well established Newtonian
mechanics. Once you have that under your belt you are propelled
into the Lagrangian formulation in a way that seems quite natural
and reveals, easily, the symmetries that lay within. This book is
written in a tight and readable style that makes even the most difficult
concepts accessable. I highly recommend it and hope that it becomes
the standard by which other mechanics texts of this level are measured.
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