عنوان

Asymptotic Approaches in Nonlinear Dynamics

(Number (ISBN

9783642720796

(Number (ISBN

9783642720819

Number

b407518

Title Proper

Asymptotic Approaches in Nonlinear Dynamics

General Material Designation

[Book]

Other Title Information

New Trends and Applications /

First Statement of Responsibility

by Jan Awrejcewicz, Igor V. Andrianov, Leonid I. Manevitch.

Place of Publication, Distribution, etc.

Berlin, Heidelberg :

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg,

Date of Publication, Distribution, etc.

1998.

Series Title

Springer Series in Synergetics,

Volume Designation

69

ISSN of Series

0172-7389 ;

Text of Note

1. Introduction: Some General Principles of Asymptotology. -- 1.1 An Illustrative Example -- 1.2 Reducing the Dimensionality of a System -- 1.3 Continualization -- 1.4 Averaging -- 1.5 Renormalization -- 1.6 Localization -- 1.7 Linearization -- 1.8 Padé Approximants -- 1.9 Modern Computers and Asymptotic Methods -- 1.10 Asymptotic Methods and Teaching Physics -- 1.11 Problems and Perspectives -- 2. Discrete Systems -- 2.1 The Classical Perturbation Technique: an Introduction -- 2.2 Krylov-Bogolubov-Mitropolskij Method -- 2.3 Equivalent Linearization -- 2.4 Analysis of Nonconservative Nonautonomous Systems -- 2.5 Nonstationary Nonlinear Systems -- 2.6 Parametric and Self-Excited Oscillation in a Three-Degree-of-Freedom Mechanical System -- 2.7 Modified Poincaré Method -- 2.8 Hopf Bifurcation -- 2.10 Normal Modes of Nonlinear Systems with n Degrees of Freedom -- 2.11 Nontraditional Asymptotic Approaches -- 2.12 Padé Approximants -- 3. Continuous Systems -- 3.1 Continuous Approximation for a Nonlinear Chain -- 3.2 Homogenization Procedure in the Nonlinear Dynamics of Thin-Walled Structures -- 3.3 Averaging Procedure in the Nonlinear Dynamics of Thin-Walled Structures -- 3.4 Bolotin-Like Approach for Nonlinear Dynamics -- 3.5 Regular and Singular Asymptotics in the Nonlinear Dynamics of Thin-Walled Structures -- 3.6 One-Point Padé Approximants Using the Method of Boundary Condition Perturbation -- 3.7 Two-Point Padé Approximants: A Plate on Nonlinear Support -- 3.8 Solitons and Soliton-Like Approaches in the Case of Strong Nonlinearity -- 3.9 Nonlinear Analysis of Spatial Structures -- 4. Discrete-Continuous Systems -- 4.1 Periodic Oscillations of Discrete-Continuous Systems with a Time Delay -- 4.2 Simple Perturbation Technique -- 4.3 Nonlinear Behaviour of Electromechanical Systems -- General References -- Detailed References (d).

0

Text of Note

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.

International Standard Book Number

9783642720819

Title

Springer eBooks

Engineering mathematics.

Mathematical physics.

Mechanics, applied.

Mechanics.

Physics.

Awrejcewicz, J., (Jan)

Andrianov, Igor V.

Manevitch, Leonid I.

SpringerLink (Online service)

Date of Transaction

20190301074400.0

Electronic name

[Book]

Y