Ebook: Nonlinear Mechanics, Groups and Symmetry

This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincaré--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems.
This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.

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This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincar?--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems.
This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.

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This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincar?--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems.
This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-12
Vector Fields, Algebras and Groups Generated by a System of Ordinary Differential Equations and their Properties....Pages 13-50
Decomposition of Systems of Ordinary Differential Equations....Pages 51-114
Asymptotic decomposition of systems of ordinary differential equations with a small parameter....Pages 115-158
Asymptotic Decomposition of Almost Linear Systems of Differential Equations with Constant Coefficients and Perturbations in the Form of Polynomials....Pages 159-218
Asymptotic Decomposition of Differential Systems with Small Parameter in the Representation Space of Finite-dimensional Lie Group....Pages 219-258
Asymptotic Decomposition of Differential Systems where Zero Approximation has Special Properties....Pages 259-304
Asymptotic Decomposition of Pfaffian Systems with a Small Parameter....Pages 305-338
Back Matter....Pages 339-382

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This unique monograph deals with the development of asymptotic methods of perturbation theory, making wide use of group- theoretical techniques. Various assumptions about specific group properties are investigated, and are shown to lead to modifications of existing methods, such as the Bogoliubov averaging method and the Poincar?--Birkhoff normal form, as well as to the formulation of new ones. The development of normalization techniques of Lie groups is also treated. The wealth of examples demonstrates how these new group theoretical techniques can be applied to analyze specific problems.
This book will be of interest to researchers and graduate students in the field of pure and applied mathematics, mechanics, physics, engineering, and biosciences.

Content:
Front Matter....Pages i-ix
Introduction....Pages 1-12
Vector Fields, Algebras and Groups Generated by a System of Ordinary Differential Equations and their Properties....Pages 13-50
Decomposition of Systems of Ordinary Differential Equations....Pages 51-114
Asymptotic decomposition of systems of ordinary differential equations with a small parameter....Pages 115-158
Asymptotic Decomposition of Almost Linear Systems of Differential Equations with Constant Coefficients and Perturbations in the Form of Polynomials....Pages 159-218
Asymptotic Decomposition of Differential Systems with Small Parameter in the Representation Space of Finite-dimensional Lie Group....Pages 219-258
Asymptotic Decomposition of Differential Systems where Zero Approximation has Special Properties....Pages 259-304
Asymptotic Decomposition of Pfaffian Systems with a Small Parameter....Pages 305-338
Back Matter....Pages 339-382
....