Kenneth Meyer, Glen Hall, Dan Offin

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 399
• Erscheinungstermin: 5. Dezember 2008
• Englisch
• ISBN-13: 9780387097244
• Artikelnr.: 37286538

Autorenporträt

Ken Meyer  has a long history of working in Hamiltonian differential equations and the N-body problem.  He has over 100 papers published.     Daniel Offin is an active researcher in the theory of Hamiltonian systems using variational methods. He has made some important contributions to celestial mechanics using the Maslov index.

Inhaltsangabe

Beginnings.- Hamiltonian Systems.- Celestial Mechanics.- The Restricted Problem.- Topics in Linear Theory.- Local Geometric Theory.- Symplectic Geometry.- Special Coordinates.- Poincaré's Continuation Method.- Normal Forms.- Bifurcations of Periodic Orbits.- Stability and KAM Theory.- Variational Techniques.

Rezensionen

"The book begins as an elementary introduction to the theory of Hamiltonian systems, taking as a starting point Hamiltonian systems of differential equations and explaining the interesting features they have with the help of classical examples. ... the book can be used at an advanced undergraduate or beginning graduate level as an introduction to these subjects, in particular when one is interested in their impact on classical (celestial) mechanics." (Johannes Giannoulis, zbMATH 1372.70002, 2017)