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Author: Ronald E. Mickens
Publisher: World Scientific
ISBN: 9810222920
Category : Science
Languages : en
Pages : 340
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Book Description
This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.
Author: Ronald E. Mickens
Publisher: World Scientific
ISBN: 9810222920
Category : Science
Languages : en
Pages : 340
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Book Description
This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.
Author: G.C. Layek
Publisher: Springer
ISBN: 8132225562
Category : Mathematics
Languages : en
Pages : 632
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Book Description
The book discusses continuous and discrete systems in systematic and sequential approaches for all aspects of nonlinear dynamics. The unique feature of the book is its mathematical theories on flow bifurcations, oscillatory solutions, symmetry analysis of nonlinear systems and chaos theory. The logically structured content and sequential orientation provide readers with a global overview of the topic. A systematic mathematical approach has been adopted, and a number of examples worked out in detail and exercises have been included. Chapters 1–8 are devoted to continuous systems, beginning with one-dimensional flows. Symmetry is an inherent character of nonlinear systems, and the Lie invariance principle and its algorithm for finding symmetries of a system are discussed in Chap. 8. Chapters 9–13 focus on discrete systems, chaos and fractals. Conjugacy relationship among maps and its properties are described with proofs. Chaos theory and its connection with fractals, Hamiltonian flows and symmetries of nonlinear systems are among the main focuses of this book. Over the past few decades, there has been an unprecedented interest and advances in nonlinear systems, chaos theory and fractals, which is reflected in undergraduate and postgraduate curricula around the world. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering.
Author: Albert C. J. Luo
Publisher: Springer Science & Business Media
ISBN: 1441957545
Category : Technology & Engineering
Languages : en
Pages : 458
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Book Description
Dynamical Systems: Discontinuous, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuses on the most recent advances in all three areas, with particular emphasis on recent analytical, numerical and experimental research and its results. Real dynamical system problems, such as the behavior of suspension systems of railways, nonlinear vibration and applied control in coal manufacturing, along with the multifractal spectrum of LAN traffic, are discussed at length, giving the reader a sense of real-world instances where these theories are applied. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay also contains material on time-delay systems as they relate to linear switching, dynamics of complex networks, and machine tools with multiple boundaries. It is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.
Author: Abba B. Gumel
Publisher: American Mathematical Soc.
ISBN: 0821898620
Category : Mathematics
Languages : en
Pages : 322
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Book Description
This volume contains the proceedings of the AMS Special Session on Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, in honor of Ronald Mickens's 70th birthday, held January 9-10, 2013, in San Diego, CA. Included are papers on design and analysis of discrete-time and continuous-time dynamical systems arising in the natural and engineering sciences, in particular, the design of robust nonstandard finite-difference methods for solving continuous-time ordinary and partial differential equation models, the analytical and numerical study of models that undergo nonlinear oscillations, as well as the design of deterministic and stochastic models for epidemiological and ecological processes. Some of the specific topics covered in the book include the analysis of deterministic and stochastic SIR-type models, the assessment of cost-effectiveness of vaccination problems, finite-difference methods for oscillatory dynamical systems (including the Schrödinger equation and Brusselator system), the design of exact and elementary stable finite-difference methods, the study of a two-patch model with Allee effects and disease-modified fitness, the study of the delay differential equation model with application to circadian rhythm and the application of some special functions in the solutions of some problems arising in the natural and engineering sciences. A notable feature of the book is the collection of some relevant open problems, intended to help guide the direction of future research in the area.
Author: Ronald E. Mickens
Publisher: World Scientific
ISBN: 981429165X
Category : Mathematics
Languages : en
Pages : 261
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Book Description
This unique book provides a concise presentation of many of the fundamental strategies for calculating approximations to the oscillatory solutions of "truly nonlinear" (TNL) oscillator equations. The volume gives a general overview of the author's work on harmonic balance, iteration and combined linearization-averaging methods. However, full discussions are also presented on parameter expansion procedures and a first-order averaging technique for TNL oscillators. The calculational basis of each method is clarified by applying them to a set of standard TNL oscillator equations. This allows a direct comparison to be made among the various methods. The book is self-contained and therefore suitable for both classroom use and self-study by students and professionals who desire to learn, understand, and apply this technique to the field of nonlinear oscillations.
Author: Vincenzo Cutello
Publisher: World Scientific
ISBN: 981270938X
Category : Mathematics
Languages : en
Pages : 642
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Book Description
Industrial mathematics is evolving into an important branch of mathematics. Mathematicians, in particular in Italy, are becoming increasingly aware of this new trend and are engaged in bridging the gap between highly specialized mathematical research and the emerging demand for innovation from industry. The contributions in this volume provide both R&D workers in industry with a general view of existing skills, and academics with state-of-the-art applications of mathematics to real-world problems, which may also be incorporated in advanced courses.
Author: Maurizio Falcone
Publisher: World Scientific
ISBN: 9814490377
Category : Mathematics
Languages : en
Pages : 249
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Book Description
The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.
Author: Vratislav Kafka
Publisher: World Scientific
ISBN: 9814491977
Category : Technology & Engineering
Languages : en
Pages : 241
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Book Description
This monograph presents an original concept of constitutive modeling of a wide variety of materials that are microscopically heterogeneous and macroscopically homogeneous. From one point of view it is a generalization of the fictitious classical 'series' and 'parallel' models; the author's model covers as special cases real structures of two-phase materials with inclusions in a matrix, or with both substructures being continuous or discontinuous. From another point of view it is a special case of a model with tensorial internal variables. Concrete structures are characterized by specific structural parameters that can be determined by simple macroscopic tests. Examples of applications to plasticity, reology, shape memory and continuum damage, as well as to metallic polycrystalline materials and concrete and fiber-reinforced materials, are demonstrated.
Author: L S Shtemenko
Publisher: World Scientific
ISBN: 9814497843
Category : Science
Languages : en
Pages : 261
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Book Description
This volume deals with the propagation of three-dimensional shock waves and their reflection from curved walls. It is divided into two parts. The first part presents a ray method. This is based on the expansion of fluid properties in power series at an arbitrary point on the shock front. Continuous fractions are used. Results for shock propagation in non-uniform fluids are given.The second part discusses the shock reflection from a concave body. The important shock-focusing problem is included. The work is supported by both numerical and experimental results. Many interesting features, such as formation of a jet, vortices and the appearance of disturbances on the shock front, are discussed.Besides shock waves in gases, the distinctive features of shock propagation through a weakly ionized plasma are considered.
Author: Berardino D'acunto
Publisher: World Scientific Publishing Company
ISBN: 9813106417
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics. Finite-difference methods for parabolic, hyperbolic as well as elliptic partial differential equations are discussed.A gradual and inductive approach to the numerical concepts has been used, such that the presentation of the theory is easily accessible to upper-level undergraduate and graduate students. Special attention has been given to the applications, with many examples and exercises provided along with solutions. For each type of equation, physical models are carefully derived and presented in full details.Windows programs developed in C++ language have been included in the accompanying CD-ROM. These programs can be easily modified to solve different problems, and the reader is encouraged to take full advantage of the innovative features of this powerful development tool.
