Limit search to available items
Book Cover
E-book
Author Meyer, Kenneth R. (Kenneth Ray), 1937-

Title Introduction to Hamiltonian dynamical systems and the N-body problem / Kenneth R. Meyer, Glen R. Hall, Dan Offin
Edition 2nd ed
Published New York : Springer Science+Business Media, ©2009

Copies

Description 1 online resource (xiii, 399 pages) : illustrations
Series Applied mathematical sciences ; v. 90
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 90.
Contents Hamiltonian systems -- Equations of celestal mechanics -- Linear Hamiltonian systems -- Topics in linear theory -- Exterior algebra and differential forms -- Symplectic transformations -- Special coordinates -- Geometric theory -- Continuation of solutions -- Normal forms -- Bifurcations of periodic orbits -- Variational techniques -- Stability and KAM theory -- Twist maps and invariant circle
Summary 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
Bibliography Includes bibliographical references (pages 389-396) and index
Notes Print version record
In Springer eBooks
Subject Hamiltonian systems.
Many-body problem.
MATHEMATICS -- Differential Equations -- General.
Hamiltonian systems.
Many-body problem.
Hamiltonian systems
Many-body problem
Form Electronic book
Author Hall, Glen R.
Offin, Daniel C. (Daniel Clyde), 1953-
LC no. 2008940669
ISBN 9780387097244
0387097244
0387097236
9780387097237