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, etc. 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.

Contents:

• Introduction to Stability Theory
• Bifurcation Analysis of Eigenvalues
• Stability Boundary of General System Dependent on Parameters
• Bifurcation Analysis of Roots and Stability of Characteristic Polynomial Dependent on Parameters
• Vibrations and Stability of Conservative System
• Gyroscopic Stabilization
• Linear Hamiltonian Systems
• Mechanical Effects Associated with Bifurcations and Singularities
• Stability of Periodic Systems Dependent on Parameters
• Stability Boundary of General Periodic System
• Instability Domains of Oscillatory System with Small Parametric Excitation and Damping
• Stability Domains of Non-Conservative System under Small Parametric Excitation

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Readership: Graduate students, academics, researchers and practitioners in aerospace, naval, civil and mechanical engineering.

"The book is an excellent and most valuable contribution, which I warmly recommend to graduate students and university professors, as well as to researchers and industrial engineers interested in multiparameter stability theory and its applications in mechanics. I expect that this book will serve as an inspiration for studies of new problems, effects, and phenomena associated with instabilities, and that it will provide a new entry to classical problems as well."

Professor Niels Olhoff Structural and Multidisciplinary Optimization

"... it is a very important and high-quality book. It represents a major contribution to the multi-parameter bifurcation theory of eigenvalues. Since Bolotin's pioneering book on nonconservation problems on the theory of elastic stability, not many books appeared at such a high level, such as this one. It beautifully summarizes the results of the authors' investigations performed for decades. The authors successfully analyze singularities of stability boundaries and provide consistent and in-depth descriptions of several most interesting mechanical effects. These include gyroscopic stabilization, instability transfer between the eigenvalue branches, paradox of destabilization by a small damping, disappearance of flutter instability, parametric resonance in periodically excited systems, to name a few."

Professor Isaac Elishakoff Meccanica

�This book has succeeded in bringing qualitative results of the famous Russian school of applied mathematics to stability theory making these results quantitative and applicable � Without hesitation I can warmly recommend the book. I have no doubt that it will fulfil what the authors hope at the end of their preface � �to promote studies of new problems, effects, and phenomena associated with instabilities and catastrophes, and give a fresh view to classical problems.�� Read Full Review

Wolfhard Kliem Mathematical Reviews

�This book is highly recommended for researchers involved in the stability investigation of physical systems, because it explains the theory from the basic facts up to a sophisticated level.�

Prof Alois Steindl Technical University of Vienna

�The material covered in the book could be used as a basis for a graduate course in mechanical, aerospace or civil engineering, as well as in applied mathematics courses on stability. Researchers in those fields will also find this book an important addition to the existing literature. To all those the book is warmly recommended. It is my opinion that it will become a classic in the field.�

Teodor M Atanackovic Theoretical and Applied Mechanics

�This book succeeds in bringing qualitative results of the famous Russian school of applied mathematics to stability theory, making these results quantitative and applicable ... applications play a major role in this book. This feature makes it of great value, especially for graduate students and engineers ... Without hesitation I can warmly recommend the book.�

Mathematical Reviews

�This book is highly recommended for researchers involved in the stability investigation of physical systems, because it explains the theory from the basic facts up to a sophisticated level.�

Zentralblatt MATH

�This book reviewed is an excellent representative both of the mathematical outlook just described and of the close Russian-style interaction between abstract geometrical thinking and specific engineering applications ... The text is clearly written and the mathematics attractively set out with plenty of clear and instructive diagrams: an enjoyable book to read.�