Classical and Celestial Mechanics: The Recife Lectures

Classical and Celestial Mechanics: The Recife Lectures

by Hildeberto Cabral
     
 

ISBN-10: 0691050228

ISBN-13: 9780691050225

Pub. Date: 09/23/2002

Publisher: Princeton University Press

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,

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Overview

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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Product Details

ISBN-13:
9780691050225
Publisher:
Princeton University Press
Publication date:
09/23/2002
Series:
Mathematical Sciences Ser.
Pages:
384
Product dimensions:
6.18(w) x 9.80(h) x 1.23(d)

Table of Contents

Foreword
Preface
Central Configurations and Relative Equilibria for the N-Body Problem1
App. AThe Area of a Triangle26
App. BMathematica Code for the Four-Body Problem29
App. CMathematica Code for the Planar Five-Body Problem30
Singularities of the N-Body Problem35
Lectures on the Two-Body Problem63
Normal Forms of Hamiltonian Systems and Stability of Equilibria117
Poincare's Compactification and Applications to Celestial Mechanics171
The Motion of the Moon205
App. ACanonical Transformation to Jacobi Coordinates230
App. BMACSYMA Program for the Intermediate Orbit233
App. CMACSYMA Program for Inclination234
App. DMACSYMA Program for First Order Terms in e235
Lectures on Geometrical Methods in Mechanics239
Momentum Maps and Geometric Phases281
Bifurcation from Families of Periodic Solutions351
References381
Index383

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