11R5. Dynamics of Synchronising Systems. - RF Nagaev (Dachny pr 9-2-66, St Petersburg, 198255, Russia). Springer-Verlag, Berlin. 2003. 326 pp. ISBN 3-540-44195-6. $149.00.
Reviewed by I Andrianov (Inst fur Allgemeine Mechanik, RWTH, Templergraben 64, Aachen, D-52056, Germany).
This book is monograph on the use of the averaging technique for solving the problems of theoretical, quantum and applied mechanics.
The book is aimed at both graduate and postgraduate students as well as researchers in mechanics and physics with university or equivalent education. It is assumed that the reader has a basic knowledge of analytical mechanics, theory of nonlinear oscillations, rigid-body dynamics, quantum mechanics and electrical engineering, as well as of mathematics in the framework of a basic course taught at a technical university.
The book is divided into 11 chapters.
Chapter 1 is devoted to the concept of local integrability and consideration of possibilities of the choice of small parameters.
Chapter 2 contains a brief description of mechanical and electromechanical systems that can be considered as being conservative.
In Chapter 3 and 4 the single-and multivariable systems in “action-angle” variables are analyzed.
In Chapter 5 multifrequency averaging of the system with a multidimensional rapidly rotating phase is carried out by a modified averaging procedure.
Usage of canonical averaging of the equations of quantum mechanics, in particular the Schro¨dinger’s equation with various potentials, made it possible to obtain a solution in a more appropriate form than on the basis of the spectral analysis (Chapter 6).
In Chapters 7, 8, and 10 the problems of weak interactions of quasiconservative dynamic systems are studied. Interesting effects of synchronization are discovered and studied.
Periodic solutions in problems of excitation of mechanical oscillations form the subject of Chapter 11.
It is noteworthy that all solutions obtained are valid for finite, but relatively extended time intervals.
The book is very interesting from the standpoint of practically usable important results as well as for further development of averaging procedure. The subject index is informative, but somewhat short. The quality of the figures is high, but, unfortunately, no captions are included. References contain mainly papers and books written in Russian, just as Russian books now have been translated into English. Moreover, practically all-Russian journals referred to are cover-to-cover translated into English. For example, MTT is translated as Mechanics of Solids, PMM as PMM J Appl Math Mech, etc. It may therefore be more natural and convenient for readers to refer to English translations.
This skillfully written book is a reader-friendly and well-organized textbook in the field of mathematical mechanics. As a rule, each section includes a pedagogical introduction.
Dynamics of Synchronising Systems is highly recommended for purchase by both individuals and libraries.
