This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations.

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"It is a book on nonlinear ordinary differential equations strongly focusing on physical and mechanical aspects. This orientation certainly introduces a new point of view on the subject. To my opinion of the reviewer, this is also the strongest argument to read and buy this book ... . Certainly, the book can be strongly recommended to all readers interested in the integration of nonlinear mechanical systems and, in particular, in synchronisation problems." (Hans Troger, Zentralblatt MATH, Vol. 1099 (1), 2007)

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