Predictability, Stability, and Chaos in N-Body Dynamical Systems (eBook, PDF)

Redaktion: Roy, Archie E.

• Format: PDF

Produktbeschreibung

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 616
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781468459975
• Artikelnr.: 43982811

Inhaltsangabe

I: Aspects of Chaos.- Chaos in a Restricted, Charged Four-Body Problem.- Chaos in the Three-Body Problem.- A New Route to Chaos: Generation of Spiral Characteristics.- Chaos in the N-Body Problem of Stellar Dynamics.- Chaos, Stability, and Predictability in Newtonian Dynamics.- Predictability, Stability, and Chaos in Dynamical Systems.- Analytical Framework in Poincaré Variables for the Motion of the Solar System.- Origin of Chaos and Orbital Behaviour in Slowly Rotating Triaxial Models.- II: Dynamics of Asteroids, Comets, and Meteors.- Modelling: An Aim and a Tool for the Study of the Chaotic Behaviour of Asteroidal and Cometary Orbits.- Mapping Models for Hamiltonian Systems with Application to Resonant Asteroid Motion.- A Model for the Study of Very-High-Eccentricity Asteroidal Motion: The 3:1 Resonance.- The Location of Secular Resonances.- Temporary Capture into Resonance.- Applications of the Restricted Many-Body Problem to Binary Asteroids.- The Wavelet Transform as Clustering Tool for the Determination of Asteroid Families.- Delivery of Meteorites from the V6 Secular Resonance Region Near 2 AU.- The Dynamics of Meteoroid Streams.- Perturbation Theory, Resonance, Librations, Chaos, and Halley's Comet.- Rotational Behaviour of Comet Nuclei.- III: Dynamics of Natural and Artificial Satellites.- The Moon's Physical Librations - Part 1: Direct Gravitational Perturbations.- The Moon's Physical Librations - Part II: Non-Rigid Moon and Direct Non-Gravitational Perturbations.- Significant High Number Commensurabilities in the Main Lunar Problem: A Postscript to a Discovery of the Ancient Chaldeans.- Moon's Influence on the Transfer from the Earth to a Halo Orbit Around L1.- First Order Theory of Perturbed Circular Motion: An Application to ArtificialSatellites.- Poincaré-Similar Variables Including J2-Secular Effects.- Measuring the Lack of Integrability of the J2 Problem for Earth's Satellites.- The Effects of the J3-Harmonic (Pear Shape) on the Orbits of a Satellite.- Stability of Satellites in Spin-Orbit Resonances and Capture Probabilities.- Statistical Analysis of the Effects of Close Encounters of Particles in Planetary Rings.- The Three-Dipole Problem.- The N-Dipole Problem and the Rings of Saturn.- Long-Time Predictions of Satellite Orbits by Numerical Integration.- Chaos in Coorbital Motion.- IV: The Three-Body Problem.- Remarkable Termination Orbits of the Restricted Problem.- Periodic Orbits in the Isosceles Three-Body Problem.- Quasi-Periodic Orbits as a Substitute of Libration Points in the Solar System.- Stability Zones Around the Triangular Lagrangian Points.- Chaotic Trajectories in the Restricted Problem of Three Bodies.- New Formulations of the Sitnikov Problem.- Periodic Solutions for the Elliptic Planar Restricted Three-Body Problem: A Variational Approach.- Hill-Type Stability and Hierarchical Stability of the General Three-Body Problem.- Equilibrium Connections on the Triple Collision Manifold.- Orbits Asymptotic to the Outermost KAM in the Restricted Three-Body Problem.- V: Selected Topics in Dynamics.- A New Interpretation of Collisions in the N-Body Problem.- An Impulsional Method to Estimate the Long-Term Behaviour of a Perturbed System: Application to a Case of Planetary Dynamics.- Improved Bettis Methods for Long-Term Prediction.- Application of Spherically Exact Algorithms to Numerical Predictability in Two-Body Problems.- Are There Irregular Families of Characteristic Curves?.- Non-Linearity in the Angles-Only Initial Orbit Determination Problem.- A Perturbation of the RelativisticKepler Problem.- Integrable Three-Dimensional Dynamical Systems and the Painlevé Property.- Generic and Nongeneric Hopf Bifurcation.- The Chaotic Motion of a Rigid Body Rotating About a Fixed Point.- Participants and Speakers.- Author Index.