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Frequency Methods in Oscillation Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 933/5 ( reviews)

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Book Synopsis Frequency Methods in Oscillation Theory by : G.A. Leonov

Download or read book Frequency Methods in Oscillation Theory written by G.A. Leonov. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to nonlocal theory of nonlinear oscillations. The frequency methods of investigating problems of cycle existence in multidimensional analogues of Van der Pol equation, in dynamical systems with cylindrical phase space and dynamical systems satisfying Routh-Hurwitz generalized conditions are systematically presented here for the first time. To solve these problems methods of Poincaré map construction, frequency methods, synthesis of Lyapunov direct methods and bifurcation theory elements are applied. V.M. Popov's method is employed for obtaining frequency criteria, which estimate period of oscillations. Also, an approach to investigate the stability of cycles based on the ideas of Zhukovsky, Borg, Hartmann, and Olech is presented, and the effects appearing when bounded trajectories are unstable are discussed. For chaotic oscillations theorems on localizations of attractors are given. The upper estimates of Hausdorff measure and dimension of attractors generalizing Doudy-Oesterle and Smith theorems are obtained, illustrated by the example of a Lorenz system and its different generalizations. The analytical apparatus developed in the book is applied to the analysis of oscillation of various control systems, pendulum-like systems and those of synchronization. Audience: This volume will be of interest to those whose work involves Fourier analysis, global analysis, and analysis on manifolds, as well as mathematics of physics and mechanics in general. A background in linear algebra and differential equations is assumed.

Physical Fundamentals of Oscillations

2018-04-16 Technology & Engineering
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Release : 2018-04-16
Genre : Technology & Engineering
Kind : eBook
Book Rating : 549/5 ( reviews)

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Book Synopsis Physical Fundamentals of Oscillations by : Leonid Chechurin

Download or read book Physical Fundamentals of Oscillations written by Leonid Chechurin. This book was released on 2018-04-16. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces possibly the most compact, simple and physically understandable tool that can describe, explain, predict and design the widest set of phenomena in time-variant and nonlinear oscillations. The phenomena described include parametric resonances, combined resonances, instability of forced oscillations, synchronization, distributed parameter oscillation and flatter, parametric oscillation control, robustness of oscillations and many others. Although the realm of nonlinear oscillations is enormous, the book relies on the concept of minimum knowledge for maximum understanding. This unique tool is the method of stationarization, or one frequency approximation of parametric resonance problem analysis in linear time-variant dynamic systems. The book shows how this can explain periodic motion stability in stationary nonlinear dynamic systems, and reveals the link between the harmonic stationarization coefficients and describing functions. As such, the book speaks the language of control: transfer functions, frequency response, Nyquist plot, stability margins, etc. An understanding of the physics of stability loss is the basis for the design of new oscillation control methods for, several of which are presented in the book. These and all the other findings are illustrated by numerical examples, which can be easily reproduced by readers equipped with a basic simulation package like MATLAB with Simulink. The book offers a simple tool for all those travelling through the world of oscillations, helping them discover its hidden beauty. Researchers can use the method to uncover unknown aspects, and as a reference to compare it with other, for example, abstract mathematical means. Further, it provides engineers with a minimalistic but powerful instrument based on physically measurable variables to analyze and design oscillatory systems.

Further Insights into Oscillation Theory

2021-07-27 Technology & Engineering
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Release : 2021-07-27
Genre : Technology & Engineering
Kind : eBook
Book Rating : 978/5 ( reviews)

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Book Synopsis Further Insights into Oscillation Theory by : Nikolai Verichev

Download or read book Further Insights into Oscillation Theory written by Nikolai Verichev. This book was released on 2021-07-27. Available in PDF, EPUB and Kindle. Book excerpt: The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods.

Asymptotic Methods in the Theory of Non-linear Oscillations

1961 Science
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Release : 1961
Genre : Science
Kind : eBook
Book Rating : 507/5 ( reviews)

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Book Synopsis Asymptotic Methods in the Theory of Non-linear Oscillations by : Nikolaĭ Nikolaevich Bogoli︠u︡bov

Download or read book Asymptotic Methods in the Theory of Non-linear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov. This book was released on 1961. Available in PDF, EPUB and Kindle. Book excerpt:

College Physics for AP® Courses

2015-07-31 Physics
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Release : 2015-07-31
Genre : Physics
Kind : eBook
Book Rating : 932/5 ( reviews)

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Book Synopsis College Physics for AP® Courses by : Irna Lyublinskaya

Download or read book College Physics for AP® Courses written by Irna Lyublinskaya. This book was released on 2015-07-31. Available in PDF, EPUB and Kindle. Book excerpt: "This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. ... This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems."--Website of book.

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