Introduction To Hamiltonian Dynamical Systems And The N Body Problem

Author : Kenneth R. Meyer,Daniel C. Offin
Publisher : Springer
Page : 384 pages
File Size : 42,6 Mb
Release : 2017-05-04
Category : Mathematics
ISBN : 9783319536910

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth R. Meyer,Daniel C. Offin Pdf

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)

Author : Kenneth Meyer,Glen Hall,Dan Offin
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 49,6 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9780387097244

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth Meyer,Glen Hall,Dan Offin Pdf

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.

Author : Kenneth Meyer,Glen Hall
Publisher : Unknown
Page : 312 pages
File Size : 50,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475740743

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth Meyer,Glen Hall Pdf

Author : Kenneth Meyer,Glen Hall,Dan Offin
Publisher : Springer
Page : 0 pages
File Size : 42,5 Mb
Release : 2010-11-29
Category : Mathematics
ISBN : 1441918868

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Kenneth Meyer,Glen Hall,Dan Offin Pdf

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.

Author : Michael J. C. Gordon,Robin Milner,Christopher P. Wadsworth
Publisher : Springer
Page : 180 pages
File Size : 43,9 Mb
Release : 1979
Category : Computers
ISBN : UOM:39015002044942

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Introduction to Hamiltonian Dynamical Systems and the N-Body Problem by Michael J. C. Gordon,Robin Milner,Christopher P. Wadsworth Pdf

Based on the notes from a graduate course taught to students in mathematics and mechanical engineering, this text takes students who had some basic knowledge of differential equations and leads them through a systematic grounding in the theory of Hamiltonian systems, an introduction to the theory of integrals and reduction.

Author : Kenneth R. Meyer
Publisher : Springer
Page : 149 pages
File Size : 48,9 Mb
Release : 2006-11-17
Category : Mathematics
ISBN : 9783540480730

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Periodic Solutions of the N-Body Problem by Kenneth R. Meyer Pdf

The N-body problem is the classical prototype of a Hamiltonian system with a large symmetry group and many first integrals. These lecture notes are an introduction to the theory of periodic solutions of such Hamiltonian systems. From a generic point of view the N-body problem is highly degenerate. It is invariant under the symmetry group of Euclidean motions and admits linear momentum, angular momentum and energy as integrals. Therefore, the integrals and symmetries must be confronted head on, which leads to the definition of the reduced space where all the known integrals and symmetries have been eliminated. It is on the reduced space that one can hope for a nonsingular Jacobian without imposing extra symmetries. These lecture notes are intended for graduate students and researchers in mathematics or celestial mechanics with some knowledge of the theory of ODE or dynamical system theory. The first six chapters develops the theory of Hamiltonian systems, symplectic transformations and coordinates, periodic solutions and their multipliers, symplectic scaling, the reduced space etc. The remaining six chapters contain theorems which establish the existence of periodic solutions of the N-body problem on the reduced space.

Author : Jurgen Moser,Jürgen Moser,Eduard Zehnder
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 52,5 Mb
Release : 2005
Category : Combinatorial dynamics
ISBN : 9780821835777

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Notes on Dynamical Systems by Jurgen Moser,Jürgen Moser,Eduard Zehnder Pdf

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.

Author : H.S. Dumas,K.R. Meyer,D.S. Schmidt
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461384489

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Hamiltonian Dynamical Systems by H.S. Dumas,K.R. Meyer,D.S. Schmidt Pdf

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Author : R.S MacKay,J.D Meiss
Publisher : CRC Press
Page : 808 pages
File Size : 47,6 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9781000156898

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Hamiltonian Dynamical Systems by R.S MacKay,J.D Meiss Pdf

Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

Author : Donald Saari,Zhihong Xia
Publisher : American Mathematical Soc.
Page : 240 pages
File Size : 42,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821805664

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Hamiltonian Dynamics and Celestial Mechanics by Donald Saari,Zhihong Xia Pdf

This book contains selected papers from the AMS-IMS-SIAM Joint Summer Research Conference on Hamiltonian Systems and Celestial Mechanics held in Seattle in June 1995. The symbiotic relationship of these two topics creates a natural combination for a conference on dynamics. The topics covered include twist maps, the Aubrey-Mather theory, Arnold diffusion, qualitative and topological studies of systems, and variational methods, as well as specific topics such as Melnikov's procedure and the singularity properties of particular systems. As one of the few books that addresses both Hamiltonian systems and celestial mechanics, this volume offers emphasis on new issues and unsolved problems. Many of the papers give new results, yet the editors purposely included some exploratory papers based on numerical computations, a section on unsolved problems, and papers that pose conjectures while developing what is known. It features open research problems, and papers on central configurations.

Author : B.A. Steves,A.J. Maciejewski,M. Hendry
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 52,8 Mb
Release : 2006-09-22
Category : Science
ISBN : 9781402047060

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Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems by B.A. Steves,A.J. Maciejewski,M. Hendry Pdf

Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.

Author : David Betounes
Publisher : Springer Science & Business Media
Page : 686 pages
File Size : 40,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475749717

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Differential Equations: Theory and Applications by David Betounes Pdf

This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. The accompanying CD contains Maple worksheets for the exercises, and special Maple code for performing various tasks. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.

Author : Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque
Publisher : Springer
Page : 399 pages
File Size : 55,7 Mb
Release : 2007-11-06
Category : Science
ISBN : 9781402063565

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Numerical Continuation Methods for Dynamical Systems by Bernd Krauskopf,Hinke M. Osinga,Jorge Galan-Vioque Pdf

Path following in combination with boundary value problem solvers has emerged as a continuing and strong influence in the development of dynamical systems theory and its application. It is widely acknowledged that the software package AUTO - developed by Eusebius J. Doedel about thirty years ago and further expanded and developed ever since - plays a central role in the brief history of numerical continuation. This book has been compiled on the occasion of Sebius Doedel's 60th birthday. Bringing together for the first time a large amount of material in a single, accessible source, it is hoped that the book will become the natural entry point for researchers in diverse disciplines who wish to learn what numerical continuation techniques can achieve. The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.

Author : Heinz Hanßmann
Publisher : Springer
Page : 242 pages
File Size : 43,7 Mb
Release : 2006-10-18
Category : Mathematics
ISBN : 9783540388968

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Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems by Heinz Hanßmann Pdf

This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.

Author : Henk Broer,Floris Takens
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 43,9 Mb
Release : 2010-10-20
Category : Mathematics
ISBN : 9781441968708

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Dynamical Systems and Chaos by Henk Broer,Floris Takens Pdf

Over the last four decades there has been extensive development in the theory of dynamical systems. This book aims at a wide audience where the first four chapters have been used for an undergraduate course in Dynamical Systems. Material from the last two chapters and from the appendices has been used quite a lot for master and PhD courses. All chapters are concluded by an exercise section. The book is also directed towards researchers, where one of the challenges is to help applied researchers acquire background for a better understanding of the data that computer simulation or experiment may provide them with the development of the theory.