The Dynamical Behaviour of our Planetary System

by Rudolf Dvorak (Editor), Jacques Henrard (Editor)

Overview

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 and recent topics which are considered as a major breakthrough in numerical dynamics: symplectic methods of numerical integration of Hamiltonian systems, and methods for spectral analysis of numerically computed orbits leading to refined tools for the detection and evaluation of chaos. The dynamics of the asteroid belt and other small objects, a fast-moving topic with important implications for the origin and evolution of the Solar System, is also extensively covered. The volume will be of interest to mathematicians and physicists interested in Hamiltonian mechanics and in the dynamics of the Solar System.

Product Details

ISBN-13:	9780792345480
Publisher:	Springer-Verlag New York, LLC
Publication date:	04/30/1997
Edition description:	Partly Reprinted from Celestia ed.
Pages:	428
Product dimensions:	6.14(w) x 9.21(h) x 1.00(d)

Table of Contents

Preface. Theoretical Dynamics. Scattering by Resonances; A. Neishtadt. Non-Integrability in Hamiltonian Mechanics; S. Ichtiaroglou. Regular and Irregular Periodic Orbits; G. Contopoulos, E. Grousouzakou. Universal Properties of Escape in Dynamical Systems; C. Siopis, et al. Numerical Methods of Analysis. Mapping and Dynamical Systems; M. Sidlichovský. A New Fast Fourier Method for Evaluating Fourier Spectra at Arbitrary Frequencies; K. Wodnar. Planets and Satellites. On the Use of Analytical Theories in the Calculation of Precession-Nutation; P. Bretagnon. Asteroids. The Nekhoroshev Theorem and the Asteroid Belt Dynamical System; A. Morbidelli, M. Guzzo. Frequency Modified Fourier Transform and its Application to Asteroids; M. Sidlichovský, D. Nesvorný. The Trojan Problem; B. Érdi. Dynamical Transport to Planet-Crossing Orbits; Ch. Froeschlé. Review of the Dynamics in the Kirkwood Gaps; M. Moons. Miscellaneous. Open Problems on the Eve of the Next Millennium; V. Szebehely. Limit of Comprehension, Reference Frames and General Relativity; H. Eichhorn. Theoretical Dynamics. Stable Chaos: A First Model; A. Lemaître. Transport in Perturbed Integrable Hamiltonian Systems and the Fractality of Phase Space; H. Varvoglis, et al. Equilibria Bifurcations of Satellite Orbits; V.W. Kudielka. Numerical Methods of Analysis. Fast Lyapunov Indicators. Comparison with Other Chaos Indicators. Application to Two and Four Dimensional Maps; E. Lega, C. Froeschlé. Asteroid Motion near the 2:1 Resonance: A Symplectic Mapping Approach; J. Hadjidemetriou, A. Lemaître. Symplectic Integrators for Hill's Lunar Problem; J. Waldvogel. Rotation Number and Global Stability of Symplectic Integrator; Yi-Sui Sun, Ji-Lin Zhou. Planets and Satellites. On a Global Expansion of the Planar Disturbing Function; C. Beaugé. Links Between Time Scales Using Barycentric Relativistic Ephemerides; X. Moisson. Orbital Stability of Planetary Quasi-Satellites; S. Mikkola, K. Innanen. Alternative Derivations of Perturbations with Use of a Mixed Reference-Plane System: Application to the Motion of the Orbit Plane of Hyperion; P.J. Message. Astrodynamic Study of the Earth Rotation; C. Marchal. Asteroids. Orbital Evolution of Asteroids in the Hecuba Gap; S. Ferraz-Mello, T.A. Michtchenko. A Study of the Local Lyapunov Numbers for Orbits in the Outer Solar System; E. Lohinger. Miscellaneous. On the Influence of Supernova Shockfronts on the Stability of the Solar System; W. Schaffenberger, A. Hanslmeier. Henri Poincaré: A Decisive Contribution to Special Relativity; C. Marchal. Periodic Orbits in the Sitnikov Problem; J. Kallrath, et al.

Editorial Reviews

Contains papers from the March 1996 colloquium, in sections on theoretical dynamics, numerical methods of analysis, planets and satellites, asteroids, and miscellaneous aspects. Subjects include regular and irregular periodic orbits, the use of analytic theories, frequency modified Fourier transform and its application to asteroids, links between time scales using barycentric relativistic ephemerides, Henri Poincar<'e>'s contribution to special relativity, and the influence of supernova shockfronts on the stability of the solar system. Partly reprinted from "Celestial Mechanics and Dynamical Astronomy", vol. 65, nos. 1-2, 1996/7. No index. Annotation c. by Book News, Inc., Portland, Or.

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