New Developments in the Dynamics of Planetary Systems

by Dvorak, Rudolf; Henrard, Jacques

• ISBN13: 9780792369660
• ISBN10: 0792369661
• Format: Hardcover
• Copyright: 2001-09-01
• Publisher: Kluwer Academic Pub

Summary

The papers in this volume cover a large range of questions concerning the dynamics of objects of the Solar System from theoretical Hamiltonian Mechanics to the study of the dynamical behaviour of specific objects with a strong emphasis on the detection, causes and effects of chaotic behaviour. Several papers describe the very latest contributions in two very lively topics; symplectic method of numerical integration of Hamiltonian systems and methods for special analysis of computed orbits leading to refined tools for the detection and evaluation of chaos. The dynamics of the asteroid belt and of NEOs (near Earth objects), two important topics with implications on the evolution of planetary systems and on the assessment of probabilities of catastrophic collisions, are also covered. This volume will be of interest to mathematicians and physicists interested in Hamiltonian mechanics and in the dynamics of planetary systems.

Table of Contents

Preface	1	(2)
Statistics for Twenty-First Century Astrometry	3	(14)
W. H. Jefferys
Synthetic Proper Elements for Outer Main Belt Asteroids	17	(30)
Z. Knezevic
A. Milani
Invariant Tori in the Secular Motions of the Three-Body Planetary Systems	47	(28)
U. Locatelli
A. Giorgilli
Improvements of Planetary Theories Over 6000 Years	75	(8)
J. Chapront
The Distribution of Energy Perturbations at Planetary Close Encounters	83	(10)
G. B. Valsecchi
A. Milani
G.F. Gronchi
S. R. Chesley
Dynamics of Small Earth-Approachers on Low-Eccentricity Orbits and Implications for their Origins	93	(20)
P. Michel
Ch. Froeschle
The Phase Space Structure Around L4 in the Restricted Three-Body Problem	113	(12)
Z. Sandor
B. Erdi
C. Efthymiopoulos
Why Do Trojan ASCS (not) Escape?	125	(12)
R. Dvorak
K. Tsiganis
The 2/1 and 3/2 Resonant Asteroid Motion: A Symplectic Mapping Approach	137	(14)
J. Hadjidemetriou
G. Voyatzis
Twist and Non-Twist Bifurcations in a System of Coupled Oscillators	151	(10)
G. Stagika
S. Ichtiaroglou
The Mel'nikov Subharmonic Function and the Non-Existence of Analytic Integrals in Non-Autonomous Systems	161	(6)
E. Meletlidou
On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: A Very Sensitive Tool	167	(30)
C. Froeschle
E. Lega
Crossing of Various Cantori	197	(14)
G. Contopoulos
M. Harsoula
N. Voglis
Fractal Dimensions as Chaos Indicators	211	(16)
F. Freistetter
Normal Form Invariants Around Spin-Orbit Periodic Orbits	227	(16)
A. Celletti
C. Falcolini
The Third Integral in a Self-Consistent Galactic Model	243	(22)
G. Contopoulos
C. Efthymiopoulos
N. Voglis
Counterrotating Galaxies and Memory of Cosmological Initial Conditions	265	(14)
N. Voglis
M. Harsoula
Ch. Efthymiopoulos
The Family P12 of the Three-Body Problem - The Simplest Family of Periodic Orbits, with Twelve Symmetries Per Period	279	(20)
C. Marchal
The Caledonian Symmetrical Double Binary Four-Body Problem I: Surfaces of Zero-Velocity using the Energy Integral	299	(20)
A.E. Roy
B.A. Steves
Application of the Nonrestricted Three-bodies Problem to the Stellar System ζ UMA	319	(6)
N.A. Solovaya
E. M. Pittich
Periodic Solutions of the Planetary 5:2 Resonance Three-body Problem	325	(4)
T. Michtchenko
S. Ferraz-Mello
Limits of Stability for Planets in Double Star Systems Using the Fast Lyapunov Indicators	329	(8)
E. Pilat-Lohinger
On a Fokker-Planck Approach to Asteroidal Transport	337	(4)
K. Tsiganis
A. Anastasiadis
H. Varvoglis
Fractality in a Galactic Model	341	(8)
J.F. Navarro
Jacques Henrard
Transformation Methods fo Trigonometric Parallaxes	349	(12)
H. Smith, Jr
The Search for Exosolar systems	361	(2)
P.K. Seidelmann
The Two Fixed Centers Problem Revisited	363	(4)
H. Varvoglis
Ch. Vozikis
K. Wodnar
E. Dimitriadou
The Phase Space Structure of the General Sitnikov Problem	367
J. Kallrath
R. Dvorak