Applied Mathematical Sciences

Introduction to Hamiltonian Dynamical Systems and the N-Body 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 N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body 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 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)

“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 Román-Roy, Zentralblatt MATH, Vol. 1179, 2010)


Table of contents (14 chapters)

  • Hamiltonian Systems

    Meyer, Kenneth (et al.)

    Pages 1-25

  • Equations of Celestial Mechanics

    Meyer, Kenneth (et al.)

    Pages 27-44

  • Linear Hamiltonian Systems

    Meyer, Kenneth (et al.)

    Pages 45-68

  • Topics in Linear Theory

    Meyer, Kenneth (et al.)

    Pages 69-115

  • Exterior Algebra and Differential Forms

    Meyer, Kenneth (et al.)

    Pages 117-132

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-0-387-09724-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-0-387-09723-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Hamiltonian Dynamical Systems and the N-Body Problem
Authors
Series Title
Applied Mathematical Sciences
Series Volume
90
Copyright
2009
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-09724-4
DOI
10.1007/978-0-387-09724-4
Hardcover ISBN
978-0-387-09723-7
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XIII, 399
Topics