Modern problems of mechanics, Collected papers
Proceedings of the Steklov Institute of Mathematics, 2016, vol. 295, 351 pp.
Abstract
The volume presents studies on various issues in mechanics and dynamical systems theory, including the self-similar piston problem in a Prandtl–Reuss elastoplastic medium with special properties, homogenization of acoustic equations for a heterogeneous layered medium consisting of creep materials, spectral stability of shock waves in singular limits of smooth heteroclinic solutions to an extended system of equations, and stability of periodic orbits of a planar Birkhoff billiard. The problem of Arnold diffusion, dynamics of nonholonomic systems, integrable systems in analytical mechanics, and problems of the KAM theory in infinite-dimensional Hamiltonian systems are also discussed.
The volume is of interest to researchers, postgraduates, and students specializing in analytical mechanics and continuum mechanics.
Citation:
Kozlov V. V., Sergeev A. G., Modern problems of mechanics, Collected papers, Proceedings of the Steklov Institute of Mathematics, 2016, vol. 295, 351 pp.
Dynamical systems on honeycombs
Traffic and granular flow '13, Springer, 2015, pp. 441–452
Abstract
Stochastic and deterministic versions of a discrete dynamical system on a necklace network are investigated. This network contains several contours. There are three cells and a particle on each contour. The particle occupies one of the cells and, at each step, it makes an attempt to move to the next cell in the direction of movement. As well as on neighboring contours the particles move in accordance with rules of stochastic or deterministic type. We prove that the behavior of the model with a rule of the first type is stochastic only at the beginning, and after a time interval the behavior becomes purely deterministic. The system with a rule of the first type reaches a stationary mode which depends on the initial state. The average velocity of particles and other characteristics of the dynamical systems are studied.
Citation:
Kozlov V. V., Buslaev A. P., Tatashev A. G., Yashina M. V., Dynamical systems on honeycombs, Traffic and granular flow '13, Springer, 2015, pp. 441–452
Asymptotic solutions of strongly nonlinear systems of differential equations
Translated from the 2009 Russian second edition [first edition: MR1457796] by Lester J. Senechal. Springer Monographs in Mathematics. Springer, Heidelberg, 2013, xx+262 pp.
Abstract
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Citation:
Kozlov V. V., Furta S. D., Asymptotic solutions of strongly nonlinear systems of differential equations, Translated from the 2009 Russian second edition [first edition: MR1457796] by Lester J. Senechal. Springer Monographs in Mathematics. Springer, Heidelberg, 2013, xx+262 pp.
Osnovaniya statisticheskoi mekhaniki i raboty Puankare, Erenfestov i fon Neimana
in A. Puankare, T. and P. Erenfesty, Dzh. fon Neiman, Raboty po statisticheskoi mekhanike, Moscow–Izhevsk: Institute of Computer Science, 2011, 249–279 pp.
Abstract
Citation:
Kozlov V. V., Smolyanov O. G., Osnovaniya statisticheskoi mekhaniki i raboty Puankare, Erenfestov i fon Neimana, in A. Puankare, T. and P. Erenfesty, Dzh. fon Neiman, Raboty po statisticheskoi mekhanike, Moscow–Izhevsk: Institute of Computer Science, 2011, 249–279 pp.
Asymptotic expansions of solutions of strongly nonlinear systems of differential equations
Moscow–Izhevsk: Regular and Chaotic Dynamics, Institute of Computer Science, 2009, 312 pp.
Abstract
Citation:
Kozlov V. V., Furta S. D., Asymptotic expansions of solutions of strongly nonlinear systems of differential equations, Moscow–Izhevsk: Regular and Chaotic Dynamics, Institute of Computer Science, 2009, 312 pp.
Proceedings of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow August 25-30, 2006)
Dordrecht Springer, 2006, 512 pp.
Abstract
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This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence held in Moscow, August 25-30, 2006. The study of vortex motion is of great interest to fluid and gas dynamics; since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important. The last few decades have shown that serious possibilities for progress in the research of real turbulent vortex motions are essentially related to the combined use of mathematical methods, computer simulation and laboratory experiments. These approaches have led to a series of interesting results which allow us to study these processes from new perspectives. Based on this principle, the papers collected in this proceedings volume present new results on theoretical and applied aspects and processes of formation and evolution of various flows, wave and coherent structures in gas and fluid. Much attention is given to the studies of nonlinear regular and chaotic regimes of vortex interactions, advective and convective motions. The contributors are leading scientists engaged in fundamental and applied aspects of the above mentioned fields.
Citation:
Borisov A. V., Kozlov V. V., Mamaev I. S., Proceedings of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow August 25-30, 2006), Dordrecht Springer, 2006, 512 pp.
Mathematical aspects of classical and celestial mechanics
Dynamical systems. III, Encyclopaedia Math. Sci., 3, Ed. 3, Springer-Verlag, Berlin, 2006, xiv+518 pp.
Abstract
Citation:
Arnold V. I., Kozlov V. V., Neishtadt A. I., Mathematical aspects of classical and celestial mechanics, Dynamical systems. III, Encyclopaedia Math. Sci., 3, Ed. 3, Springer-Verlag, Berlin, 2006, xiv+518 pp.
Lyapunov's first method for strongly nonlinear systems of differential equations
Nonlinear mechanics, eds. V. M. Matrosov, V. V. Rumyantsev, A. V. Karapetyan. Moscow: Fizmatlit, 2001, 89–113 pp.
Abstract
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Citation:
Kozlov V. V., Furta S. D., Lyapunov's first method for strongly nonlinear systems of differential equations, Nonlinear mechanics, eds. V. M. Matrosov, V. V. Rumyantsev, A. V. Karapetyan. Moscow: Fizmatlit, 2001, 89–113 pp.
Principle of relativity and forces of inertia
Theoretical Mechanics, Collection of scientific and methodological papers, no. 21, MPI, Moscow, 1999, pp. 16–23
Abstract
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Citation:
Kozlov V. V., Harin A. O., Principle of relativity and forces of inertia, Theoretical Mechanics, Collection of scientific and methodological papers, no. 21, MPI, Moscow, 1999, pp. 16–23
Hamiltonian systems with three degrees of freedom and hydrodynamics
Hamiltonian systems with three or more degrees of freedom (S'Agaró, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 1999, vol. 533, pp. 127–133
Abstract
According to Stephan Banach, the possibilities of a mathematician are determined by his abilities to operate with analogies of different levels. The first level is the ability to see and to use the analogies between different problems. The next level is constituted by the analogies between theories. And finally only can be considered as high class mathematicians those who are able to use analogies between analogies.
Citation:
Kozlov V. V., Hamiltonian systems with three degrees of freedom and hydrodynamics, Hamiltonian systems with three or more degrees of freedom (S'Agaró, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 1999, vol. 533, pp. 127–133
Asymptotic expansions of solutions of strongly nonlinear systems of differential equations
Izdatel'stvo Moskovskogo Universiteta, Moscow, 1996, 244 pp.
Abstract
Citation:
Kozlov V. V., Furta S. D., Asymptotic expansions of solutions of strongly nonlinear systems of differential equations, Izdatel'stvo Moskovskogo Universiteta, Moscow, 1996, 244 pp.
Symmetries, topology and resonances in Hamiltonian mechanics
Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 31. Springer-Verlag, Berlin, 1996, xii+378 pp.
Abstract
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Citation:
Kozlov V. V., Symmetries, topology and resonances in Hamiltonian mechanics, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 31. Springer-Verlag, Berlin, 1996, xii+378 pp.
Symmetries, topology and resonances in Hamiltonian mechanics
Izhevsk: Publishing House of Udmurt State University, 1995, 429 pp.
Abstract
pdf (19.86 Mb)
Citation:
Kozlov V. V., Symmetries, topology and resonances in Hamiltonian mechanics, Izhevsk: Publishing House of Udmurt State University, 1995, 429 pp.
Mathematical aspects of classical and celestial mechanics
Dynamical systems. III, Encyclopaedia Math. Sci., 3, 2nd ed., Springer-Verlag, Berlin, 1993, xiv+291 pp.
Abstract
Citation:
Arnold V. I., Kozlov V. V., Neishtadt A. I., Mathematical aspects of classical and celestial mechanics, Dynamical systems. III, Encyclopaedia Math. Sci., 3, 2nd ed., Springer-Verlag, Berlin, 1993, xiv+291 pp.
Billiards. A genetic introduction to the dynamics of systems with impacts
Izdatel'stvo Moskovskogo Universiteta, Moscow, 1991, 168 pp.
Abstract
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Citation:
Kozlov V. V., Treschev D. V., Billiards. A genetic introduction to the dynamics of systems with impacts, Izdatel'stvo Moskovskogo Universiteta, Moscow, 1991, 168 pp.
Billiards. A genetic introduction to the dynamics of systems with impacts
Translations of Mathematical Monographs, 89. Providence, RI: American Mathematical Society (AMS), 1991, viii+171 pp.
Abstract
Billiard systems arise in many problems of mechanics and physics, some of them being described in the introduction. The authors have chosen a genetic approach, which consists in replacing a single-sided constraint imposed on the system by a field of elastic and dissipative forces. When the elastic and dissipative coefficients tend to infinity, the motion with fixed initial values tends on finite time intervals to a motion with impacts. The celebrated theorem of Birkhoff on the estimating of the number of distinct periodic trajectories of a convex elastic billiard is proved in a variational way, and some conditions for stability of the periodic trajectories are given. A chapter is dedicated to the Hill equation, obtained in the problem of the motion of the perigee of the moon and encountered also in problems of the stability of periodic motions with impacts. An important problem is the integrability of systems of billiard type. Old and new integrable problems, as the elliptic billiard, the billiard in affine Weyl cells, a harmonic oscillator inside an ellipse, billiards on surfaces of constant curvatures are described. The book is written in a clear and careful style and completely describes the problems from the physical phenomenon to the mathematical solution.
Citation:
Kozlov V. V., Treschev D. V., Billiards. A genetic introduction to the dynamics of systems with impacts, Translations of Mathematical Monographs, 89. Providence, RI: American Mathematical Society (AMS), 1991, viii+171 pp.