Chaotic Worlds

by Steves, B. A.; Maciejewski, A. J.; Hendry, M.

• ISBN13: 9781402047046
• ISBN10: 1402047045
• Format: Hardcover
• Copyright: 2006-08-15
• Publisher: Springer Nature

Summary

The gravitational N-body problem dominates much of theoretical astrophysics. It arises in problems ranging from the motion of artificial and natural satellites to the behaviour of stars in star clusters and galaxies. In the past, research in Celestial Mechanics has focused on analytical and numerical studies of ordered systems, with chaotic behaviour or disorder being the fascinating anomaly. Recently, however, scientists have begun to forge the link between order and disorder: designing new methods to recognise chaos' signature and developing new theories on the sources of chaotic behaviour. They are applying these techniques successfully to solve real-world problems in solar system dynamics, galactic dynamics and other areas of physics such as particle acceleration. Based on the recent NATO Advanced Study Institute "Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems", this state of the art textbook, written by internationally renowned experts, provides an invaluable reference volume for all students and researchers in gravitational n-body systems. The contributions are especially designed to give a systematic development from the fundamental mathematics which underpin modern studies of ordered and chaotic behaviour in n-body dynamics to their application to real motion in planetary systems. This volume presents an up-to-date synoptic view of the subject.

Table of Contents

Preface	vii
Lecturers	xi
Part I Tools of Order
Canonical perturbation theory for nearly integrable systems	1	(42)
Antonio Giorgilli, Ugo Locatelli
Periodic orbits in gravitational systems	43	(38)
John D. Hadjedemetriou
Periodic solutions in Gravitational Problems and the Structure of Solution Space	81	(22)
P.J. Message
General properties of three-body systems with Hill-type stability	103	(28)
C. Marchal
Part II Tools for investigation of Chaos and its sources
The fine structure of Hamiltonian systems revealed using the Fast Lyapunov Indicator	131	(36)
Claude Froeschlé, Elena Lega
Fourier analysis of chaotic motions and applications to Celestial mechanics	167	(36)
Massimiliano Guzzo
Part III Sources of Chaos
Basics of regularization theory	203	(28)
Alessandra Celletti
Order and chaos in Satellite encounters	231	(24)
Jörg Waldvogel
Part IV Applications
Regular motions in extra-solar planetary systems	255	(34)
S. Ferraz-Mello, T.A. Micchtchenko, C. Beaugé
Tides on Europa	289	(18)
Richard Greenberg
Numerical evaluation of Love's solution for Tidal amplitude	307	(18)
T.A. Hurford, S. Frey, R. Greenberg
On the general solutions of Hilbert-Einstein field equations in vacuum	325	(8)
C. Marchal
List of Participants	333