Asymptotic Approaches in Nonlinear Dynamics: New Trends and Applications (Springer Series in Synergetics, 69)

How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? B. Birkhoff [52J This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this manuscript have not been treated but just mentioned in the literature. Providing a state-of-the-art review of asymptotic applications, this book will prove useful as an introduction to the field for novices as well a reference for specialists. Asymptotic methods of solving mechanical and physical problems have been developed by many authors. For example, we can refer to the excel­ lent courses by A. Nayfeh [119-122]' M. Van Dyke [154], E.J. Hinch [94J and many others [59, 66, 95, 109, 126, 155, 163, 50d, 59dJ. The main features of the monograph presented are: 1) it is devoted to the basic principles of asymp­ totics and its applications, and 2) it deals with both traditional approaches (such as regular and singular perturbations, averaging and homogenization, perturbations of the domain and boundary shape) and less widely used, new approaches such as one- and two-point Pade approximants, the distributional approach, and the method of boundary perturbations. This book covers developments in the field of the theory of oscillations from the diverse viewpoints, reflecting the field's multidisciplinary nature. Addressing researchers in mechanics, physics, applied mathematics, and engineering, as well as students, the book gives an introduction to the state of the art in this area and to various applications. For the first time a treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Padé approximations is presented. Because of its wealth of interesting examples this book will prove useful as an introduction to the field for novices and a reference for specialists. This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists. An examination of developments in the field of the theory of oscillations from diverse viewpoints, reflecting the field's multidisciplinary nature. It provides an introduction to the state of the art in this area and to various applications. Introduction: Some General Principles of Asymptotology Discrete Systems Continual Systems Discrete-Continuous Systems General References Detailed References Index.