Impact of Modern Dynamics in Astronomy: Proceedings of the Iau Colloquium 172 Held in Namur, Belgium, July 1998

by Iau Colloquium 1998 (Namur, Belgium); Mello, S. Ferraz; Henrard, Jacques; Henrard, Jacques; Ferraz-Mello, Sylvio

• ISBN13: 9780792358428
• ISBN10: 0792358422
• Edition: Reprint
• Format: Hardcover
• Copyright: 2000-08-01
• Publisher: Kluwer Academic Pub

Summary

This volume of proceedings contains review and research papers concerning the impact of modern dynamics in astronomy. Modern dynamics is playing an increasing role in the solution of problems raised by astronomical observations. This new relationship is being fostered by recent discoveries of new systems, such as the Kuiper belt, pulsar and star companions; by progress in theoretical dynamics, like KAM and Nekhorochev theories and adiabatic invariants; and by the dissemination of fast computers. The two main areas of applications which are discussed are 'stellar systems', including dynamics of galaxies, and 'small bodies in the solar system'. In both cases the concepts and tools of chaotic motion are considered and fully discussed. This book is an up-to-date source of information for astronomers interested in the dynamics of the solar system or of stellar systems, as well as for dynamicists who wish to understand the impact of modern theories of chaos in astronomy.

Table of Contents

Preface	ix
Cosmology
Chaos in Relativity and Cosmology	1	(16)
G. Contopoulos
N. Voglis
C. Efthymiopoulos
Bianchi Cosmologies as Dynamical Systems	17	(8)
A. Maciejewski
M. Szydlowski
Small Bodies in the Solar System
Slow and Fast Diffusion in Asteroid-Belt Resonances: A Review	25	(14)
S. Ferraz-Mello
Origin and Evolution of Near Earth Asteroids	39	(12)
A. Morbidelli
Small Bodies in the Outer Solar System	51	(4)
B. G. Marsden
The Use of Geocentric Variables to Search for Meteroid Streams and Their Parents	55	(10)
Cl. Froeschle
T. J. Jopek
G. B. Valsecchi
A Symplectic Mapping Model as a Tool to Understand the Dynamics of 2/1 Resonant Asteroid Motion	65	(12)
J. D. Hadjidemetriou
On Stable Chaos in the Asteroid Belt	77	(10)
M. Sidlichovsky
Explicit Semi-Analytical Theory of Asteroid Motion	87	(10)
I. V. Tupikova
A. A. Vakhidov
M. Soffel
On the Motion of Trapped Particles in the Vicinity of Corotation Centers	97	(10)
C. Beauge
A. Lemaitre
S. Jancart
Migration of Trans-Neptunian Objects to the Earth	107	(10)
S. I. Ipatov
Trojans in Stable Chaotic Motion	117	(10)
E. Pilat-Lohinger
R. Dvorak
Ch. Burger
Stellar Systems
Star Cluster Simulations: the State of the Art	127	(12)
S. J. Aarseth
Dimensionality of Stable and Unstable Directions in the Gravitational N-Body Problem	139	(10)
R. H. Miller
Distribution of Kolmogorov-Sinai Entropy in Self-Consistent Models of Barred Galaxies	149	(10)
H. Wozniak
D. Pfenniger
Regular and Chaotic Motion in Globular Clusters	159	(10)
D. D. Carpintero
J. C. Muzzio
F. C. Wachlin
Periodic Orbits around a Massive Straight Segment	169	(10)
A. Riaguas
A. Elipe
M. Lara
Escape from a Crisis in Fokker-Planck Models	179	(8)
S. Portegies Zwart
K. Takahashi
Building Galaxy Models with Schwarzschild Method and Spectral Dynamics	187	(8)
Honsheng Zhao
Analytical and Numerical Tools
Conditional Entropy: a Tool to Explore Phase Space	195	(16)
P. Cincotta
C. Simo
Detection of Ordered and Chaotic Motion using the Dynamical Spectra	211	(10)
N. Voglis
G. Contopoulos
C. Efthymiopoulos
Cantori, Islands and Asymptotic Curves in the Stickiness Region	221	(10)
C. Efthymiopoulos
G. Contopoulos
N. Voglis
Parallel/Vector Integration Methods for Dynamical Astronomy	231	(12)
T. Fukushima
Do Average Hamiltonians Exist?	243	(6)
S. Ferraz-Mello
Diffusion Character in Four-Dimensional Volume-Preserving Map	249	(10)
Yi-Sui Sun
Yan-Ning Fu
The Separatrix Algorithmic Map: Application to the Spin-Orbit Motion	259	(10)
I. I. Shevchenko
Canonical Variables of the Second Kind and the Reduction of the N-Body Problem	269	(12)
J. G. Bryant
Motion near the Unit Circle in the Three-Body Problem	281	(10)
R. A. Broucke
A Global Analysis of the Generalized Sitnikov Problem	291	(12)
S. R. Chesley
The Hamiltonian Dynamics of the Two Gyrostats Problem	303	(10)
F. Mondejar
A. Vigueras
Planets and Satellites
Planetary Systems	313	(4)
P. Artymowicz
Complements to Moon's Lunar Libration Theory	317	(12)
J. Chapront
M. Chapront-Touze
G. Francou
Impact of the Quadrupole Moment of the Sun on the Dynamics of the Earth-Moon System	329	(10)
E. Bois
J. F. Girard
The Effect of C22 on Orbit Energy and Angular Momentum	339	(10)
D. J. Scheeres
The Use of Lie Series in the Construction of a Perturbation Theory and Some Recent Results in the Theory of the Motion of Hyperion	349	(10)
P. J. Message
EXTENDED ABSTRACTS
Small Bodies in the Solar System
Higher Order and Iterative Theories to Compute Asteroid Mean Elements	359	(2)
Z. Knezevic
A. Milani
The Asteroid Mass Determination Project at the U.S. Naval Observatory	361	(2)
J. L. Hilton
R. C. Stone
The Asteroid Identification Problem	363	(2)
M. E. Sansaturio
A. Milani
A. La Spina
K. Muinonen
Interaction of Resonances and Yarkovsky Non-Gravitational Effects in the Asteroid Belt	365	(4)
D. Vokroulicky
P. Farinella
Target Plane Confidence Boundaries: Mathematics of the 1997 XF11 Scare	369	(2)
A. Milani
G. B. Valsecchi
A Dynamical Survey of Inner Solar System Asteroids	371	(2)
Murison
Detailled Study of the Dynamics of Fragments of Comet C/1996 B2 Hyakutake	373	(2)
E. Desvoivres
J. Klinger
A. C. Levasseur-Regourd
Proper Elements and Stability of the Trojan Asteroids	375	(2)
Ch. Burger
E. Pilat-Lohinger
R. Dvorak
A. Christaki
Dynamical Behaviour of Asteroids in the 4:1 Resonance	377	(2)
F. Lopez-Garcia
A. Brunini
Perturbations of Small Moons Orbits due to their Rotation: the Model Problem	379	(2)
K. Gozdziewski
A. J. Maciejewski
Mean-Motion Resonances in the Asteroid Belt	381	(2)
D. Nesvorny
A. Morbidelli
On the Critical Phenomena in the Dynamics of Asteroids	383	(4)
I. I. Shevchenko
Dynamics of Real Asteroids at the Hecuba Gap	387	(2)
F. Roig
S. Ferraz-Mello
Modelling Very-High-Eccentri-city Asteroidal Librations with the Andoyer Hamiltonian	389	(2)
A. Simula
S. Ferraz-Mello
C. Giordano
Stellar Systems and Galaxies
Resonant Relaxation	391	(2)
S. Tremaine
Periodic Orbits in Three-Armed Galaxies	393	(2)
P. J. GrosbØl
P. A. Patsis
Orbits in a Stackel Approximation	395	(2)
V. De Bruyne
F. Leeuwin
H. Dejonghe
Measuring Mass Loss Rates from Galactic Satellites	397	(2)
K. V. Johnston
S. Sigurdsson
L. Hernquist
Effect of Chaotic Orbits on Dynamical Friction	399	(2)
S. A. Cora
M. M. Vergne
J. C. Muzzio
Nonparametric Statistical Models of Globular Cluster Dynamics	401	(2)
W. D. Heacox
Orbits of Hipparcos Metal-Poor Stars with Well-Defined Spectroscopic Abundances	403	(2)
F. Bancken
E. Jehin
HST-FGS Astrometry of the Low Mass Binary L722-22	405	(4)
L. G. Taff
J. L. Hershey
Can Combination of `Kozai effect' and Tidal Friction Produce Close Stellar and Planetary Orbits?	409	(2)
L. G. Kiseleva
P. P. Eggleton
Simple Periodic Orbits in Elliptical Galaxies Modelled by Hamiltonians in 1-1-1 Resonances	411	(2)
J. Palacian
P. Yanguas
S. Ferrer
Planetary Systems
Moon's Planetary Perturbations	413	(2)
P. Bidart
J. Chapront
On the Construction of a Long Term Moon's Theory	415	(2)
T. V. Ivanova
A New Model of Mars Rotation from Pathfinder Data	417	(2)
S. Bouquillon
J. Souchay
Dynamics of the Mimas-Thetys System	419	(6)
S. Champenois
A Necessary Condition to the Simultaneous Correction of Celestial Reference Frames	425	(2)
M. J. Martinez Uso
F. J. Marco-Castillo
J. A. Lopez Orti
Secular Pertubations near Mean Motion Resonances	427	(2)
A. A. Christou
Dynamics of Fictitious Earth Satellites with Possible Past Value of the Ecliptic	429	(2)
N. Callegari Jr.
T. Yokoyama
E. P. Marinho
An Intermediary Periodic Orbit for Hyperion	431	(2)
I. Stellmacher
Tools
Averaging of Earth-Crossing Orbits	433	(2)
G. F. Gronchi
A. Milani
Rotational Motion of Celestial Bodies in the Relativistic Framework	435	(2)
S. Klioner
M. Soffel
Lommel Functions in some Drag-Perturbed Problem	437	(2)
S. Breiter
A. A. Jackson
Two Conjectures of G. D. Birkhoff	439	(2)
Ch. K. Mccord
K. R. Meyer
Three-Body Stability Criteria	441	(2)
J. R. Donnison
Nekhoroshev Stability in Quasi-Integrable Degenerate Hamiltonian Systems	443	(2)
M. Guzzo
Nekhoroshev-Stability of L4 and L5 in the Spatial Restricted Problem	445	(2)
G. Benettin
F. Fasso
M. Guzzo
Effective Lyapunov Numbers and Correlation Dimension in a 3-D Hamiltonian System	447	(2)
K. Tsiganis
A. Anastasiadis
H. Varvoglis
A Symplectic Integration Scheme that Allows Close Encounters between Massive Bodies	449	(2)
J. E. Chambers
Analytical Approximation of the Dissipative Standard Map	451	(2)
A. Celletti
G. Della Penna
C. Froeschle
Second Order Perturbations of Elliptic Elements with respect to the Initial Ones	453	(2)
F. J. Marco-Castillo
M. J. Martinez Uso
J. A. Lopez Orti
Miscellaneous
Zonal Harmonics of the Gravity Field in DEF-variables	455	(2)
A. Aparicio
L. Floria
On the Stability of Stationary Solutions of the Twice-Averaged Hill's Problem taking into account the Planet Oblateness	457	(2)
M. A. Vashkovyak
Study of the Normal Variational Equation in an Homogenous Field of Degree Five	459	(2)
A. Makhlouf
N. Debbah
Generalyzed Gylden-Type System in Universal DS-like TR-variables	461	(2)
L. Floria
Orbital Structure of the Two Fixed Centres Problem	463	(2)
A. Cordero
J. Martinez Alfaro
P. Vindel
Chaos in Three-Body Dynamics: Intermittency, Strange Attractor, Kolmogorov-Sinai Entropy	465
A. D. Chernin