Series on Stability, Vibration and Control of Systems, Series A - Vol. 13


Alexander P. Seyranian & Alexei A. Mailybaev

(Moscow State Lomonosov University, Russia)

World Scientific, New Jersey, 2004
xvi+403 pp. ISBN 981-238-406-5 (US$86.00,£64.00)


This book deals with fundamental problems, concepts, and methods of multiparameter stability theory with applications in mechanics. It presents recent 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, etc. The methods presented are constructive and easy to implement in computer programs.


  • 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


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.

Book reviews

"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." Read Full Review

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." Read Full Review

Professor Isaac Elishakoff

“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.” Read Full Review

Professor Alois Steindl
Zentralblatt MATH

“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.” Read Full Review

Professor 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.”  Read Full Review

Professor Wolfhard Kliem
Mathematical Reviews

“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.” Read Full Review

Professor D.R.J.Chillingworth
Journal of Sound and Vibration