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| Author | : Kenneth R. Meyer |
| Publisher | : Springer |
| Total Pages | : 384 |
| Release | : 2017-05-04 |
| Genre | : Mathematics |
| ISBN | : 3319536915 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2008-12-05 |
| Genre | : Mathematics |
| ISBN | : 0387097244 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
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 |
| Publisher | : |
| Total Pages | : 312 |
| Release | : 2014-01-15 |
| Genre | : |
| ISBN | : 9781475740745 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
| Author | : Kenneth Meyer |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2010-11-29 |
| Genre | : Mathematics |
| ISBN | : 9781441918864 |
Download Introduction to Hamiltonian Dynamical Systems and the N-Body Problem Book in PDF, ePub and Kindle
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 R. Meyer |
| Publisher | : Springer |
| Total Pages | : 149 |
| Release | : 2006-11-17 |
| Genre | : Mathematics |
| ISBN | : 3540480730 |
Download Periodic Solutions of the N-Body Problem Book in PDF, ePub and Kindle
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 |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 2005 |
| Genre | : Combinatorial dynamics |
| ISBN | : 0821835777 |
Download Notes on Dynamical Systems Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 392 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461384486 |
Download Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
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 | : Walter Craig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 450 |
| Release | : 2008-02-17 |
| Genre | : Mathematics |
| ISBN | : 1402069642 |
Download Hamiltonian Dynamical Systems and Applications Book in PDF, ePub and Kindle
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
| Author | : Kenneth Ray Meyer |
| Publisher | : |
| Total Pages | : 288 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
Download Hamiltonian Dynamical Systems Book in PDF, ePub and Kindle
This volume contains contributions by participants in the AMS-IMS-SIAM Summer Research Conference on Hamiltonian Dynamical Systems, held at the University of Colorado in June 1984. The conference brought together researchers from a wide spectrum of areas in Hamiltonian dynamics. The papers vary from expository descriptions of recent developments to fairly technical presentations with new results. Collectively, they provide an excellent survey of contemporary work in this area. The field of Hamiltonian dynamics has its roots in Newton's application of the science of dynamics to the emerging problems of orbital mechanics and in the development of celestial mechanics. Indeed, many of the talks at the conference emphasized topics directly concerned with such questions as the Newtonian $n$-body problem, the three-body problem, and the artificial earth satellite. Some speakers focused on those dynamical issues--such as integrability, KAM, and extensions of the Poincare-Birkhoff results--that emerged from celestial mechanics and extend to wider classes of dynamical systems. Other topics covered include periodic orbits with variation methods, twist and annulus maps, stable mainfold theory, almost periodic motion, and heteroclinic and homoclinic orbits. By bringing together papers from such a diverse range of topics, this book may serve to stimulate further development in this area.
| Author | : Donald Saari |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821805665 |
Download Hamiltonian Dynamics and Celestial Mechanics Book in PDF, ePub and Kindle
The symbiotic of these two topics creates a natural combination for a conference on dynamics. 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.
