Introduction to Hamiltonian Dynamical Systems and the NBody Problem
Authors: Meyer, Kenneth, Hall, Glen, Offin, Daniel C.
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 About this book

This text grew out of graduate level courses in mathematics, engineering and physics given at several 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. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincaré's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods.
The main examples treated in this text are the Nbody problem and various specialized problems like the restricted threebody problem. The theory of the Nbody problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point.
Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University.
 Reviews

From the 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 Nbody 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 wellorganized 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)
“This is an interesting book on Hamiltonian systems, which is conceived as a first course at the graduate level. … the book has two parts. The first one includes seven chapters and is more introductory in nature. … The second part contains the most interesting and advanced material of the book. … The book … constitutes a very complete course on the theory of Hamiltonian systems.” (Narciso RománRoy, Zentralblatt MATH, Vol. 1179, 2010)
 Table of contents (14 chapters)


Hamiltonian Systems
Pages 125

Equations of Celestial Mechanics
Pages 2744

Linear Hamiltonian Systems
Pages 4568

Topics in Linear Theory
Pages 69115

Exterior Algebra and Differential Forms
Pages 117132

Table of contents (14 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to Hamiltonian Dynamical Systems and the NBody Problem
 Authors

 Kenneth Meyer
 Glen Hall
 Daniel C. Offin
 Series Title
 Applied Mathematical Sciences
 Series Volume
 90
 Copyright
 2009
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9780387097244
 DOI
 10.1007/9780387097244
 Series ISSN
 00665452
 Edition Number
 2
 Number of Pages
 XIII, 399
 Topics