• De Gruyter 2013


Nonconservative Stability Problems
of Modern Physics

I have summarized the existing theoretical concepts and approaches to nonconservative stability problems on the basis of my original contributions and vision of the field in the 429-page monograph “Nonconservative stability problems of modern physics” published by De Gruyter in 2013. My monograph is already held by >1170 libraries worldwide (including Yale, UPenn, Brown, Princeton, Columbia, Cornell, BerkeleyMIT, NYU, UChicago, UMich, CaMe, JHU, Stanford, Oxford, ETH, EPFL, BNF, UPMC, Kyoto, HU Berlin, Tsinghua, Russian State Library, etc.).

The book has already got excellent reviews, for example:

“Not often appears a monograph that combines the exposition of the modern mathematical methods and their application to the study of important physical phenomena. It is a wonderful example of the excellent Moscow school of mathematical physics.”
(Prof. Ferdinand Verhulst, University of Utrecht, the Netherlands, for the Nieuw Archief voor Wiskunde, vol. 15, pp. 290-291, December 2014, pdf).

“The book is an extremely impressive and thorough treatise. It is certainly a unique and major contribution to our understanding of the stability of mechanical systems. Congratulations on this brilliant synthesis.”
(Prof. J Michael T Thompson, University of Cambridge, UK)


  • Wiley 2014


Nonlinear Physical Systems:
Spectral Analysis, Stability and Bifurcations

In order to intensify communication across different scientific communities and involve new researchers into the development of the unified non-conservative stability theory I initiated an ambitious project of organizing an international BIRS workshop at the Banff International Research Station (BIRS) for Mathematical Innovation and Discovery in Banff, Alberta, Canada. In 2012 after winning a tough competition we got a grant from BIRS and organized a very successful 5 days BIRS Research Workshop on Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems. A collection of selected articles from the participants of the Workshop has been published under Dmitry Pelinovsky and my edition by Wiley in 2014. Many participants commented that they benefited a lot from the crossdisciplinary nature of the workshop ( “Yes, I have benefited by the workshop very much. The program covered rather interdisciplinary subjects. I could lean many new things. I could also start interactions with researches of different disciplines.” – Prof. Zensho Yoshida, University of Tokyo, Japan. “The Workshop was well conceived, bringing together people in fields that are different yet similar enough for meaningful and indeed useful connections to develop.” – Prof. Sir Michael Berry, University of Bristol, UK.

  • Springer 2018

springer2018 BIGONI, DAVIDE, KIRILLOV, OLEG N. (Editors)

Dynamic Stability and Bifurcation in Nonconservative Mechanics

The book offers a unified view on classical results and recent advances in the dynamics of nonconservative systems. The theoretical fundamentals are presented systematically and include: Lagrangian and Hamiltonian formalism, non-holonomic constraints, Lyapunov stability theory, Krein theory of spectra of Hamiltonian systems and modes of negative and positive energy, anomalous Doppler effect, reversible systems, sensitivity analysis of non-self-adjoint operators, dissipation-induced instabilities, local and global instabilities. They are applied to engineering situations such as the coupled mode flutter of wings, flags and pipes, flutter in granular materials, piezoelectric mechanical metamaterials, wave dynamics of infinitely long structures, radiative damping, stability of high-speed trains, experimental realization of follower forces, soft-robot locomotion, wave energy converters, friction-induced instabilities, brake squeal, non-holonomic sailing, dynamics of moving continua, and stability of bicycles and walking robots. The book responds to a demand in the modern theory of nonconservative systems coming from the growing number of scientific and engineering disciplines including physics, fluid and solids mechanics, fluid-structure interactions, and modern multidisciplinary research areas such as biomechanics, micro- and nanomechanics, optomechanics, robotics, and material science. It is targeted at both young and experienced researchers and engineers working in fields associated with the dynamics of structures and materials. The book will help to get a comprehensive and systematic knowledge on the stability, bifurcations and dynamics of nonconservative systems and establish links between approaches and methods developed in different areas of mechanics and physics and modern applied mathematics.



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