11R7. Modern Approach to Classical Mechanics. - H Iro (Inst for Theor Phys, Johannes Kepler Univ, Linz, Austria). World Sci Publ, Singapore. Distributed in USA by World Sci Publ, River Edge NJ. 2002. 442 pp. ISBN 981-238-213-5. $58.00.

Reviewed by K Anderson (Dept of Mech Eng, Aeronaut Eng, and Mech (JEC4006), RPI, Troy NY 12180-3590).

The book covers virtually all aspects of the field of classical mechanics starting from Newton’s laws of motion for the motion of a point mass. The book progresses to the concepts of integrals of Newton’s equations of motion, which leads naturally to the concepts of energy and the potential for constants of motion such as with conservation of energy, and angular momentum. The author provides some interesting discussion of specific cases and diverges from most traditional texts with his presentation of the notion of chaos, phase space analysis, and stability analysis very early in the book. All the common subjects (central force motion, two-body gravitational problem, restricted three-body problem, simple oscillators, damped oscillators, particle collisions, and the like) are presented, as are the more advanced treatments such as Lagrangian mechanics, rigid bodies, Hamilton’s principle, Hamiltonian dynamics, and Hamilton-Jacobi theory.

The book covers a great deal of material in a relatively short and concise manner, yielding a book just over 400 pages long (which is shorter than many books that consider only a few of the individual subjects covered). The book is fairly well organized, and the author does a good job of introducing some difficult concepts in a very concise manner. The associated figures are very simple line diagrams, but are clear and well thought out. The author does not directly state the audience for which book is intended, but in this reviewer’s opinion the book should be of interest to any individual seeking basic introductory or overview level information on these subjects. As such the book provides relatively few problems, with the presentation of most theory and derivations in this text being quite condensed; formal worked-out examples are not to be found. Thus, this book would most likely not serve well as a self-standing course textbook, but may make a good supplemental reference or basic reference for those who seek a concise overview of many important classical mechanics (and not so classical, eg, chaos) topics.

What is somewhat different about Modern Approach to Classical Mechanics is the author’s continued and pervasive discussion of the fact that many (even simple) dynamic systems are chaotic and that as such, even the deterministic equations of motion presented cannot be expected to yield accurate predictions of the arbitrarily distant future. This is the “modern approach” indicated in the book’s title. In this reviewer’s opinion, some of these discussions seem a little forced and the value they bring to the text is questionable. Twenty years ago this material and approach might have been considered revolutionary and of great interest, but it is difficult to be excited about it now given that these concepts that the author stresses already are widely (although not commonly) known. Being that as it may, the author’s implicit point that practitioners should not place too much trust in deterministic equations is one that should be made more often to students and engineers (and generally does not appear in foundation level mechanics texts).