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| Author | : Georgio Eugenio Oscare Giacaglia |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 379 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461264006 |
Download Perturbation Methods in Non-Linear Systems Book in PDF, ePub and Kindle
This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ ential equations. In this respect, it appears to be a unique work. The main goal is to describe perturbation techniques, discuss their ad vantages and limitations and give some examples. The approach is founded on analytical and numerical methods of nonlinear mechanics. Attention has been given to the extension of methods to high orders of approximation, required now by the increased accuracy of measurements in all fields of science and technology. The main theorems relevant to each perturbation technique are outlined, but they only provide a foundation and are not the objective of these notes. Each chapter concludes with a detailed survey of the pertinent literature, supplemental information and more examples to complement the text, when necessary, for better comprehension. The references are intended to provide a guide for background information and for the reader who wishes to analyze any particular point in more detail. The main sources referenced are in the fields of differential equations, nonlinear oscillations and celestial mechanics. Thanks are due to Katherine MacDougall and Sandra Spinacci for their patience and competence in typing these notes. Partial support from the Mathematics Program of the Office of Naval Research is gratefully acknowledged.
| Author | : Giorgio E. O. Giacaglia |
| Publisher | : |
| Total Pages | : 369 |
| Release | : 1972 |
| Genre | : Differential equations, Nonlinear |
| ISBN | : 9783540900542 |
Download Perturbation Methods in Non-linear Systems Book in PDF, ePub and Kindle
| Author | : V.N. Bogaevski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 276 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461244382 |
Download Algebraic Methods in Nonlinear Perturbation Theory Book in PDF, ePub and Kindle
Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. Topics covered include: matrix perturbation theory; systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives. While boundary problems are not discussed, the book is clearly illustrated by numerous examples.
| Author | : Jan A. Sanders |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 259 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475745753 |
Download Averaging Methods in Nonlinear Dynamical Systems Book in PDF, ePub and Kindle
In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.
| Author | : K. W. Chang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 191 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 146121114X |
Download Nonlinear Singular Perturbation Phenomena Book in PDF, ePub and Kindle
Our purpose in writing this monograph is twofold. On the one hand, we want to collect in one place many of the recent results on the exist ence and asymptotic behavior of solutions of certain classes of singularly perturbed nonlinear boundary value problems. On the other, we hope to raise along the way a number of questions for further study, mostly ques tions we ourselves are unable to answer. The presentation involves a study of both scalar and vector boundary value problems for ordinary dif ferential equations, by means of the consistent use of differential in equality techniques. Our results for scalar boundary value problems obeying some type of maximum principle are fairly complete; however, we have been unable to treat, under any circumstances, problems involving "resonant" behavior. The linear theory for such problems is incredibly complicated already, and at the present time there appears to be little hope for any kind of general nonlinear theory. Our results for vector boundary value problems, even those admitting higher dimensional maximum principles in the form of invariant regions, are also far from complete. We offer them with some trepidation, in the hope that they may stimulate further work in this challenging and important area of differential equa tions. The research summarized here has been made possible by the support over the years of the National Science Foundation and the National Science and Engineering Research Council.
| Author | : Daomin Cao |
| Publisher | : Cambridge University Press |
| Total Pages | : 263 |
| Release | : 2021-02-18 |
| Genre | : Mathematics |
| ISBN | : 1108836836 |
Download Singularly Perturbed Methods for Nonlinear Elliptic Problems Book in PDF, ePub and Kindle
A systematic introduction to the singularly perturbed methods in the study of concentration solutions for nonlinear elliptic problems.
| Author | : Giampaolo Cicogna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 218 |
| Release | : 2003-07-01 |
| Genre | : Science |
| ISBN | : 354048874X |
Download Symmetry and Perturbation Theory in Nonlinear Dynamics Book in PDF, ePub and Kindle
has been in the of a Symmetry major ingredient development quantum perturba tion and it is a basic of the of theory, ingredient theory integrable (Hamiltonian and of the the use in context of non Hamiltonian) systems; yet, symmetry gen eral is rather recent. From the of view of nonlinear perturbation theory point the use of has become dynamics, widespread only through equivariant symmetry bifurcation in this attention has been confined to linear even theory; case, mostly symmetries. in recent the and of methods for dif Also, theory practice symmetry years ferential has become and has been to a equations increasingly popular applied of the of the book Olver This by variety problems (following appearance [2621). with is and deals of nature theory deeply geometrical symmetries general (pro vided that described i.e. in this context there is are vector no they by fields), to limit attention to linear reason symmetries. In this look the basic tools of i.e. normal book we at perturbation theory, introduced Poincar6 about and their inter a forms (first by century ago) study action with with no limitation to linear ones. We focus on the most symmetries, basic fixed the and i.e. a setting, systems having point (at origin) perturbative around thus is local.
| Author | : Reza N. Jazar |
| Publisher | : Springer Nature |
| Total Pages | : 584 |
| Release | : 2021-07-12 |
| Genre | : Technology & Engineering |
| ISBN | : 3030734625 |
Download Perturbation Methods in Science and Engineering Book in PDF, ePub and Kindle
Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.
| Author | : Richard H. Rand |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210607 |
Download Perturbation Methods, Bifurcation Theory and Computer Algebra Book in PDF, ePub and Kindle
Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.
| Author | : M. Vidyasagar |
| Publisher | : SIAM |
| Total Pages | : 515 |
| Release | : 2002-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898719185 |
Download Nonlinear Systems Analysis Book in PDF, ePub and Kindle
When M. Vidyasagar wrote the first edition of Nonlinear Systems Analysis, most control theorists considered the subject of nonlinear systems a mystery. Since then, advances in the application of differential geometric methods to nonlinear analysis have matured to a stage where every control theorist needs to possess knowledge of the basic techniques because virtually all physical systems are nonlinear in nature. The second edition, now republished in SIAM's Classics in Applied Mathematics series, provides a rigorous mathematical analysis of the behavior of nonlinear control systems under a variety of situations. It develops nonlinear generalizations of a large number of techniques and methods widely used in linear control theory. The book contains three extensive chapters devoted to the key topics of Lyapunov stability, input-output stability, and the treatment of differential geometric control theory. Audience: this text is designed for use at the graduate level in the area of nonlinear systems and as a resource for professional researchers and practitioners working in areas such as robotics, spacecraft control, motor control, and power systems.
