Frequency Methods in Oscillation Theory PDF Download
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Author: G.A. Leonov
Publisher: Springer Science & Business Media
ISBN: 9400901933
Category : Mathematics
Languages : en
Pages : 415
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Book Description
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.
Author: G.A. Leonov
Publisher: Springer Science & Business Media
ISBN: 9400901933
Category : Mathematics
Languages : en
Pages : 415
Get Book Here
Book Description
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.
Author: Leonid Chechurin
Publisher: Springer
ISBN: 3319751549
Category : Technology & Engineering
Languages : en
Pages : 262
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Book Description
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.
Author: Gennady Leonov
Publisher:
ISBN: 9789400901940
Category :
Languages : en
Pages : 420
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Book Description
Author: G.A. Leonov
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 424
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Book Description
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.
Author: Irna Lyublinskaya
Publisher:
ISBN: 9781938168932
Category : Physics
Languages : en
Pages : 1665
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Book Description
"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.
Author:
Publisher:
ISBN:
Category : Periodicals
Languages : en
Pages : 806
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Book Description
Author: Suk-Hwan Suh
Publisher: Springer Science & Business Media
ISBN: 1848003366
Category : Technology & Engineering
Languages : en
Pages : 466
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Book Description
Computer Numerical Control (CNC) controllers are high value-added products counting for over 30% of the price of machine tools. The development of CNC technology depends on the integration of technologies from many different industries, and requires strategic long-term support. “Theory and Design of CNC Systems” covers the elements of control, the design of control systems, and modern open-architecture control systems. Topics covered include Numerical Control Kernel (NCK) design of CNC, Programmable Logic Control (PLC), and the Man-Machine Interface (MMI), as well as the major modules for the development of conversational programming methods. The concepts and primary elements of STEP-NC are also introduced. A collaboration of several authors with considerable experience in CNC development, education, and research, this highly focused textbook on the principles and development technologies of CNC controllers can also be used as a guide for those working on CNC development in industry.
Author: Lei Luo
Publisher: Frontiers Media SA
ISBN: 288976723X
Category : Technology & Engineering
Languages : en
Pages : 358
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Book Description
Author: Gesong Chen
Publisher: John Wiley & Sons
ISBN: 1119129087
Category : Technology & Engineering
Languages : en
Pages : 271
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Book Description
This book is an all-in-one resource on the development and application of variable frequency transformers to power systems and smart grids. It introduces the main technical issues of variable frequency transformers (VFT) systematically, including its basic construction, theory equations, and simulation models. Readers will then gain an in-depth discussion of its control system, operation performance, low frequency power oscillation, and technical economics, before proceeding to practical implementation and future developments. The related concepts of energy revolution, third generation grids, and power system interconnection are discussed as well. The first, comprehensive introduction to variable frequency transformers (VFT) An in-depth look at the construction of VFT, with simulations and applications Demonstrates how to assess the control system and overall system performance Analyses future developments, energy revolution and power system interconnections Variable Frequency Transformers for Large Scale Power Systems is a timely overview of the state of the art for VFT as it is increasingly adopted in smart grids. It is intended for engineers and researchers specializing in power system planning and operation, as well as advanced students and industry professionals of power engineering.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 992
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Book Description
