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Introduction to Hamiltonian Dynamical Systems and the N Body Problem

Introduction to Hamiltonian Dynamical Systems and the N Body Problem Author Kenneth R. Meyer
ISBN-10 9783319536910
Release 2017-07-25
Pages 384
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This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)



Introduction to Hamiltonian Dynamical Systems and the N Body Problem

Introduction to Hamiltonian Dynamical Systems and the N Body Problem Author Kenneth Meyer
ISBN-10 9780387097244
Release 2008-12-05
Pages 399
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Arising from a graduate course taught to math and engineering students, this text provides a systematic grounding in the theory of Hamiltonian systems, as well as introducing the theory of integrals and reduction. A number of other topics are covered too.



Introduction to Hamiltonian Dynamical Systems and the N body Problem

Introduction to Hamiltonian Dynamical Systems and the N body Problem Author Kenneth Ray Meyer
ISBN-10 LCCN:2008940669
Release 2009
Pages 399
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Introduction to Hamiltonian Dynamical Systems and the N body Problem has been writing in one form or another for most of life. You can find so many inspiration from Introduction to Hamiltonian Dynamical Systems and the N body Problem also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Introduction to Hamiltonian Dynamical Systems and the N body Problem book for free.



Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems Author
ISBN-10 9781461418054
Release 2012
Pages 1858
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Mathematics of Complexity and Dynamical Systems has been writing in one form or another for most of life. You can find so many inspiration from Mathematics of Complexity and Dynamical Systems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics of Complexity and Dynamical Systems book for free.



Piecewise smooth Dynamical Systems

Piecewise smooth Dynamical Systems Author Mario Bernardo
ISBN-10 1846287081
Release 2008-01-01
Pages 482
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This book presents a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction expounds the ubiquity of such models via numerous. The results are presented in an informal style, and illustrated with many examples. The book is aimed at a wide audience of applied mathematicians, engineers and scientists at the beginning postgraduate level. Almost no mathematical background is assumed other than basic calculus and algebra.



Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems Author Gerald Teschl
ISBN-10 9780821883280
Release 2012-08-30
Pages 356
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This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.



Variational Methods and Periodic Solutions of Newtonian N body Problems

Variational Methods and Periodic Solutions of Newtonian N body Problems Author Kuo-Chang Chen
ISBN-10 MINN:31951P007547088
Release 2001
Pages 152
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Variational Methods and Periodic Solutions of Newtonian N body Problems has been writing in one form or another for most of life. You can find so many inspiration from Variational Methods and Periodic Solutions of Newtonian N body Problems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Variational Methods and Periodic Solutions of Newtonian N body Problems book for free.



Mathematical Aspects of Classical and Celestial Mechanics

Mathematical Aspects of Classical and Celestial Mechanics Author Victor V. Kozlov
ISBN-10 9783642612374
Release 2013-12-01
Pages 294
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From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989



The N Vortex Problem

The N Vortex Problem Author Paul K. Newton
ISBN-10 9781468492903
Release 2013-03-09
Pages 420
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This text is an introduction to current research on the N- vortex problem of fluid mechanics. It describes the Hamiltonian aspects of vortex dynamics as an entry point into the rather large literature on the topic, with exercises at the end of each chapter.



Local and Semi Local Bifurcations in Hamiltonian Dynamical Systems

Local and Semi Local Bifurcations in Hamiltonian Dynamical Systems Author Heinz Hanßmann
ISBN-10 354038894X
Release 2007
Pages 237
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Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n- parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.



Differential Dynamical Systems Revised Edition

Differential Dynamical Systems  Revised Edition Author James D. Meiss
ISBN-10 9781611974645
Release 2017-01-24
Pages 392
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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.÷ Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.



Notes on Dynamical Systems

Notes on Dynamical Systems Author Jürgen Moser
ISBN-10 9780821835777
Release 2005
Pages 256
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This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial $N$-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments. Jurgen Moser (1928-1999) was a professor atthe Courant Institute, New York, and then at ETH Zurich. He served as president of the International Mathematical Union and received many honors and prizes, among them the Wolf Prize in mathematics. Jurgen Moser is the author of several books, among them Stable and Random Motions in DynamicalSystems. Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.



Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds Author Taeyoung Lee
ISBN-10 9783319569536
Release 2017-09-05
Pages 539
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This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.



Regular and Chaotic Dynamics

Regular and Chaotic Dynamics Author Allan Lichtenberg
ISBN-10 9781475721843
Release 2013-03-14
Pages 692
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This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.



Dynamics in the Hill problem with applications to spacecraft maneuvers

Dynamics in the Hill problem with applications to spacecraft maneuvers Author Benjamin F. Villac
ISBN-10 UOM:39015057585286
Release 2003
Pages
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Dynamics in the Hill problem with applications to spacecraft maneuvers has been writing in one form or another for most of life. You can find so many inspiration from Dynamics in the Hill problem with applications to spacecraft maneuvers also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Dynamics in the Hill problem with applications to spacecraft maneuvers book for free.



Chaos Near Resonance

Chaos Near Resonance Author G. Haller
ISBN-10 9781461215080
Release 2012-12-06
Pages 430
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A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.



Notices of the American Mathematical Society

Notices of the American Mathematical Society Author American Mathematical Society
ISBN-10 UCSD:31822005594676
Release 1991
Pages
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Notices of the American Mathematical Society has been writing in one form or another for most of life. You can find so many inspiration from Notices of the American Mathematical Society also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Notices of the American Mathematical Society book for free.