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James MeissThis is an excellent text and reference. I know of no comparable book. Its scope is wide, and the quality of the authors is extremely high.
— James Meiss, University of Colorado, Boulder
This book brings together a number of lectures given between 1993 and 1999 as part of a special series hosted by the Federal University of Pernambuco, in which internationally established researchers came to Recife, Brazil, to lecture on classical or celestial mechanics. Because of the high quality of the results and the general interest in the lecturers' topics, the editors have assembled nine of the lectures here in order to make them available to mathematicians and students around the world. The material presented includes a good balance of pure and applied research and of complete and incomplete results. Bringing together material that is otherwise quite scattered in the literature and including some important new results, it will serve graduate students and researchers interested in Hamiltonian dynamics and celestial mechanics.
The contributors are Dieter Schmidt, Ernesto Pérez-Chavela, Mark Levi, Plácido Táboas and Jack Hale, Jair Koiller et al., Hildeberto Cabral, Florin Diacu, and Alain Albouy. The topics covered include central configurations and relative equilibria for the N-body problem, singularities of the N-body problem, the two-body problem, normal forms of Hamiltonian systems and stability of equilibria, applications to celestial mechanics of Poincaré's compactification, the motion of the moon, geometrical methods in mechanics, momentum maps and geometric phases, holonomy for gyrostats, microswimming, and bifurcation from families of periodic solutions.
|Central Configurations and Relative Equilibria for the N-Body Problem||1|
|App. A||The Area of a Triangle||26|
|App. B||Mathematica Code for the Four-Body Problem||29|
|App. C||Mathematica Code for the Planar Five-Body Problem||30|
|Singularities of the N-Body Problem||35|
|Lectures on the Two-Body Problem||63|
|Normal Forms of Hamiltonian Systems and Stability of Equilibria||117|
|Poincare's Compactification and Applications to Celestial Mechanics||171|
|The Motion of the Moon||205|
|App. A||Canonical Transformation to Jacobi Coordinates||230|
|App. B||MACSYMA Program for the Intermediate Orbit||233|
|App. C||MACSYMA Program for Inclination||234|
|App. D||MACSYMA Program for First Order Terms in e||235|
|Lectures on Geometrical Methods in Mechanics||239|
|Momentum Maps and Geometric Phases||281|
|Bifurcation from Families of Periodic Solutions||351|
"This is an excellent text and reference. I know of no comparable book. Its scope is wide, and the quality of the authors is extremely high."—James Meiss, University of Colorado, Boulder
"These lectures, in addition to containing some new significant results, perform the service of collecting together the material on diverse topics in celestial mechanics in an accessible form."—Edward Belbruno, Princeton University