Classical and Celestial Mechanics: The Recife Lectures

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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.

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What People Are Saying

James Meiss
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
Edward Belbruno
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
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Product Details

  • ISBN-13: 9780691050225
  • Publisher: Princeton University Press
  • Publication date: 9/23/2002
  • Series: Mathematical Sciences Ser.
  • Pages: 384
  • Product dimensions: 6.18 (w) x 9.80 (h) x 1.23 (d)

Table of Contents

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
References 381
Index 383
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"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

Read More Show Less

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