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Zbl 0754.70001
Hagedorn, Peter
Non-linear oscillations. Translated from the German, edited and with a preface by Wolfram Stadler. 2nd ed. (English)
[B] Oxford Engineering Science Series. 10. Oxford: Clarendon Press. xii, 311 p. (1988). ISBN 0-19-856194-6

This book deals with the study of nonlinear ordinary differential equations with special emphasis on nonlinear oscillations. It consists of five chapters. Chapter 1 examines free and forced oscillations in damped and undamped systems using as an illustration the mathematical pendulum. Different methods are presented such as perturbation methods, the Ritz method etc.\par Chapter 2 presents the Lyapunov stability theory and bifurcations. Chapter 3 is concerned with analytical approximation methods for the computation of self-excited oscillations. Chapter 4 contains a general view of Hamilton differential equations in mechanics. Chapter 5 gives an introduction to the theory of optimal control with interesting comments concerning this theory.\par At the end of each chapter a large number of references are presented. In the last part of the book, the solutions for the exercises proposed by the author are given. This book is of interest to physicists, engineers and research workers in other branches of science.
[S.Popp (Bucureşti)]

MSC 2000:: *70-01 Textbooks (mechanics of particles and systems)
70K20 Stability of nonlinear oscillations (general mechanics)
70K99 Nonlinear motions

Keywords: mathematical pendulum; perturbation methods; Ritz method; bifurcations; Hamilton differential equations; optimal control

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Zentralblatt MATH Berlin [Germany]