Predictability, Stability, and Chaos in N-Body Dynamical Systems için kapak resmi
Predictability, Stability, and Chaos in N-Body Dynamical Systems
Başlık:
Predictability, Stability, and Chaos in N-Body Dynamical Systems
ISBN:
9781468459975
Edition:
1st ed. 1991.
Yayın Bilgileri:
New York, NY : Springer US : Imprint: Springer, 1991.
Fiziksel Tanımlama:
616 p. online resource.
Series:
NATO Science Series B:, Physics ; 272
Contents:
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 Artificial Satellites -- 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 Relativistic Kepler 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.
Abstract:
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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Dil:
English