Multiparameter Stability Theory With Mechanical Applications

By: Alexei A Mailybaev, Alexander P Seyranian

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Hardcover | 5 January 2004

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420 Pages

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22.86 x 15.24 x 1.91

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Dealing with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics, this book presents: achievements and knowledge of bifurcation theory; sensitivity analysis of stability characteristics; general aspects of nonconservative stability problems; analysis of singularities of boundaries for the stability domains; stability analysis of multiparameter linear periodic systems; and optimization of structures under stability constraints. Systems with finite degrees of freedom and with continuous models are both considered. The book combines mathematical foundation with interesting classical and modern mechanical problems. A number of mechanical problems illustrating how bifurcations and singularities change the behavior of systems and lead to new physical phenomena are discussed. Among these problems, the authors consider systems of rotating bodies, tubes conveying fluid, elastic columns under the action of periodic and follower forces, optimization problems for conservative systems and more. The methods presented are constructive and easy to implement in computer programs. This book is addressed to graduate students, academics, researchers, and practitioners in aerospace, naval, civil, and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics.

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.,." excellent representative of the mathematical outlook (and of the close Russian-style interaction) between abstract geometrical thinking and specific engineering applications ..."

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Preface
Introduction to Stability Theory	p. 1
Bifurcation Analysis of Eigenvalues	p. 21
Stability Boundary of General System Dependent on Parameters	p. 83
Bifurcation Analysis of Roots and Stability of Characteristic Polynomial Dependent on Parameters	p. 117
Vibrations and Stability of Conservative System	p. 149
Gyroscopic Stabilization	p. 169
Linear Hamiltonian Systems	p. 191
Mechanical Effects Associated with Bifurcations and Singularities	p. 233
Stability of Periodic Systems Dependent on Parameters	p. 267
Stability Boundary of General Periodic System	p. 309
Instability Domains of Oscillatory System with Small Parametric Excitation and Damping	p. 333
Stability Domains of Non-Conservative System under Small Parametric Excitation	p. 365
Concluding Remarks	p. 389
Bibliography	p. 391
Index	p. 401
Table of Contents provided by Blackwell. All Rights Reserved.

Multiparameter Stability Theory With Mechanical Applications

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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