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Classical and Celestial Mechanics : The Recife Lectures - Hildeberto Cabral

Classical and Celestial Mechanics

The Recife Lectures

By: Hildeberto Cabral (Editor), Florin Diacu (Editor)

Hardcover

Published: 13th October 2002
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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 Perez-Chavela, Mark Levi, Placido Taboas 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 Poincare'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.

"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

Foreword
Preface
Central Configurations and Relative Equilibria for the N-Body Problemp. 1
The Area of a Trianglep. 26
Mathematica Code for the Four-Body Problemp. 29
Mathematica Code for the Planar Five-Body Problemp. 30
Singularities of the N-Body Problemp. 35
Lectures on the Two-Body Problemp. 63
Normal Forms of Hamiltonian Systems and Stability of Equilibriap. 117
Poincare's Compactification and Applications to Celestial Mechanicsp. 171
The Motion of the Moonp. 205
Canonical Transformation to Jacobi Coordinatesp. 230
MACSYMA Program for the Intermediate Orbitp. 233
MACSYMA Program for Inclinationp. 234
MACSYMA Program for First Order Terms in ep. 235
Lectures on Geometrical Methods in Mechanicsp. 239
Momentum Maps and Geometric Phasesp. 281
Bifurcation from Families of Periodic Solutionsp. 351
Referencesp. 381
Indexp. 383
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780691050225
ISBN-10: 0691050228
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 408
Published: 13th October 2002
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 23.5 x 15.2  x 3.18
Weight (kg): 0.71