Nagaev R.F. Dynamics of synchronising systems

Berlin — Heidelberg: Springer-Verlag, 2003 — ii + 330 p. — ISBN: 978-3-642-53655-7.The present book is based upon the monograph published in Russian by Nauka, St. Petersburg in 1996. However the present book contains an increased number of applications and this is why the sixth, ninth and eleventh chapters have been added. The sixth chapter, written by A.G. Chirkov, is concerned with a description of the averaging procedure by means of the methods of non-relativistic quantum mechanics.Particularly, this chapter is important since non-rigorous approaches of the intuitive character are still used to analyse some physical problems and they may lead to inaccuracies and, possibly, gross error. The ninth chapter is devoted to the analysis of the phenomenon of self-synchronisation of the inertial vibration exciters which are frequently used to drive modern vibrational facilities. The basis for this chapter is the material of monograph [76] published by Mashinostroenie, St. Petersburg in 1990. The last, eleventh, chapter of the present book is written by D.Yu. Skubov. Its origin is in the earlier publications by K.Sh. Khodzhaev and is also aimed at applications in the field of vibrational technology. It is worthwhile noting the peculiarity of the problems of synchronisation in electromechanical systems. The mechanism of weak interaction of electromechanical objects is of an essentially nonconservative character. Nevertheless, stable synchronous regimes can also have close extremum properties in these problems.The present book is based on "physical" reasoning. The author does not suggest principle improvements to the modern methods of the theory of nonlinear oscillations. The main objective is to find a rational means of obtaining sufficiently general averaged equations of motion which have a clear physical interpretation and are valid for a broad class of weak interaction problems of a mechanical (or other) nature. Using these equations allows one to avoid, at least to the first approximation, the necessity for cumbersome derivations. This results in a justified prediction of the character of the stable, stationary motion of the system without constructing the original equations of motion. The author hopes that the results obtained, as well as the proposed style, provide a degree of interest in terms of both science and teaching.It is assumed that the reader has a basic knowledge of analytical mechanics, rigid body dynamics, theory of nonlinear oscillations, as well as quantum mechanics and electrical engineering. The book is written primarily for researchers in Mechanics and Physics with a university or equivalent education, mathematicians specialising in the field of the theory of ordinary differential equations, as well as graduate and post-graduate students. Nevertheless, the author has tried to make the book understandable for a broad range of readers. For this reason, detailed mathematically rigorous proofs and substantiations are omitted and the special terminology related to these proofs is not included.The present book is the result of many years of activity by the author in the corresponding field of research. It brings together and, to a great extent, completes his previously published works in various journals and proceedings. The works by LI. Blekhman published in 1953-1960 years gave an initial impetus to the present research. The following colleagues and coworkers of the author: L. Kh. Akhmetshin, P.S. Goldman, V.V. Guzev, A.A. Danilin, F.F.Fazullin, K.Sh. Khodzhaev and S.D. Shatalov contributed to the research at different times. In particular, the results of Sections 1.5, 2.4, 4.6, 5.4 and 5.6 were obtained by the author together with P.S. Goldman. Many useful suggestions about the manuscript were made by A. K. Belyaev and S. McWilliam.