Yu. A. Mitropolsky's Books

Applied Asymptotic Methods in Nonlinear Oscillations

By: Yuri A. Mitropolsky,Nguyen Van Dao

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Applied Asymptotic Methods in Nonlinear Oscillations

By: Yuri A. Mitropolsky,Nguyen Van Dao

Many dynamical systems are described by differential equations that can be separated into one part, containing linear terms with constant coefficients, and a second part, relatively small compared with the first, containing nonlinear terms. Such a system is said to be weakly nonlinear. The small terms rendering the system nonlinear are referred to as perturbations. A weakly nonlinear system is called quasi-linear and is governed by quasi-linear differential equations. We will be interested in systems that reduce to harmonic oscillators in the absence of perturbations. This book is devoted primarily to applied asymptotic methods in nonlinear oscillations which are associated with the names of N. M. Krylov, N. N. Bogoli ubov and Yu. A. Mitropolskii. The advantages of the present methods are their simplicity, especially for computing higher approximations, and their applicability to a large class of quasi-linear problems. In this book, we confine ourselves basi cally to the scheme proposed by Krylov, Bogoliubov as stated in the monographs [6,211. We use these methods, and also develop and improve them for solving new problems and new classes of nonlinear differential equations. Although these methods have many applications in Mechanics, Physics and Technique, we will illustrate them only with examples which clearly show their strength and which are themselves of great interest. A certain amount of more advanced material has also been included, making the book suitable for a senior elective or a beginning graduate course on nonlinear oscillations.

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Page Count

352

Publisher

Springer Science & Business Media

Published Date

ISBN 10

9401588473

ISBN 13

9789401588478

Asymptotic Methods in Resonance Analytical Dynamics

By: Eugeniu Grebenikov,Yu. A. Mitropolsky,Y.A. Ryabov

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Asymptotic Methods in Resonance Analytical Dynamics

By: Eugeniu Grebenikov,Yu. A. Mitropolsky,Y.A. Ryabov

Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincaré. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.

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Page Count

282

Publisher

CRC Press

Published Date

ISBN 10

0203409833

ISBN 13

9780203409831

Dichotomies and Stability in Nonautonomous Linear Systems

By: Yu. A. Mitropolsky,A.M. Samoilenko,V.L. Kulik

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Dichotomies and Stability in Nonautonomous Linear Systems

By: Yu. A. Mitropolsky,A.M. Samoilenko,V.L. Kulik

Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func

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Page Count

390

Publisher

CRC Press

Published Date

ISBN 10

1482264897

ISBN 13

9781482264890

Book's by Yu. A. Mitropolsky

Applied Asymptotic Methods in Nonlinear Oscillations

Applied Asymptotic Methods in Nonlinear Oscillations

Asymptotic Methods in Resonance Analytical Dynamics

Asymptotic Methods in Resonance Analytical Dynamics

Dichotomies and Stability in Nonautonomous Linear Systems

Dichotomies and Stability in Nonautonomous Linear Systems

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