Asymptotic Methods in Resonance Analytical Dynamics PDF Download
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Author: Evgeni Aleksandrovich Grebenikov
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Evgeni Aleksandrovich Grebenikov
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Eugeniu Grebenikov
Publisher: CRC Press
ISBN: 9780203409831
Category : Mathematics
Languages : en
Pages : 282
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Book Description
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.
Author: Anatoly A. Martynyuk
Publisher: Springer
ISBN: 303007644X
Category : Mathematics
Languages : en
Pages : 198
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Book Description
The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.
Author: Sergey P. Kuznetsov
Publisher: Springer Science & Business Media
ISBN: 3642236669
Category : Science
Languages : en
Pages : 320
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Book Description
"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos. This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering. Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.
Author: Jan Awrejcewicz
Publisher: CRC Press
ISBN: 1000581276
Category : Mathematics
Languages : en
Pages : 506
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Book Description
This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.
Author: V.G. Ganzha
Publisher: Springer
ISBN: 3540451951
Category : Computers
Languages : en
Pages : 314
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Book Description
This book constitutes the refereed proceedings of the 9th International Workshop on Computer Algebra in Scientific Computing, CASC 2006. The book presents 25 revised full papers together with 2 invited papers, covering various expanding applications of computer algebra to scientific computing, the computer algebra systems themselves, and the CA algorithms. Topics addressed are studies in Gröbner bases, polynomial algebra, homological algebra, quantifier elimination, celestial mechanics, and more.
Author: Jan Awrejcewicz
Publisher: CRC Press
ISBN: 100058125X
Category : Mathematics
Languages : en
Pages : 411
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Book Description
This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 628
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Book Description
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
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Book Description
Author: Jan Awrejcewicz
Publisher: Springer Science & Business Media
ISBN: 364272079X
Category : Science
Languages : en
Pages : 321
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Book Description
This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.
