From Newton to Chaos

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.

Inhalt
Prelude: Poincaré's Contribution to Chance and Chaos.- One: Planetary Theory.- Perturbation Theory: Techniques and Limitations.- Quantitative Methods in Classical Perturbation Theory.- Jacobi Geometry and Chaos in N-Body Systems.- Proper Elements and Stable Chaos.- Mechanisms of Generation of Chaos in the Solar System.- On the Convergence of the Disturbing Function.- Improving the Classical Expansion of the Disturbing Function.- The Great Inequality in a Hamiltonian Planetary Theory.- Stability Over Exponentially Long Times in the Planetary Problem.- Interlude: Remarkable and Spectacular Comets.- Two: Dynamics of Asteroids, Comets and Meteors.- From Order to Chaos: Clustering and Diffusion Processes for Small Bodies in the Solar System.- Depletion of the Asteroid Belt at Resonances.- On the Depletion of the Outer Asteroid Belt.- The Chaotic Zone Connected With the 5/2 Mean Motion Resonance.- The Influence of Chaos on the Evolution of the Minor Bodies of the Solar System.- Project Criss-Cross: A Preliminary Analysis.- Meteoroid Stream Dynamics.- Interlude: From Newton's Adjustable Clock to Poincaré's Chaos.- Three: Dynamics of Natural and Artificial Satellites.- Chaotic Motion in Hill's Lunar Problem.- Hunting for Periodic Orbits Close to that of the Moon in the Restricted Circular Three Body Problem.- Orbital Elements of a Satellite Moving in the Potential of an Oblate Spheroid.- Integrability and Chaos in the Classical 2-Centre Field J2-Approximation.- Analytic Non-integrability and the J2-Problem.- Guidelines for a General Treatment of the J2 Problem in DS Variables with True Anomaly Type Fictitious Time.- Second Order Perturbations Due to the Gravity Potential of a Planet.- Perturbation Expansions Around Elliptic Fixed Points in the Spin-Orbit Problem.-Moment Formalism for the Radiative Force Evaluation.- Optimization of Spacecraft Trajectories Using Nonlinear Programming.- Four: The Three Body Problem.- Order Out of Chaos in the Three Body Problem: Regions of Escape.- Chaos in the Hyperbolic Restricted Three Body Problem.- Types of Motion and Stability of Hierarchical Triple Star Systems.- On the Role of the Moment of Inertia in Three Body Scattering.- The Bicircular Model Near the Triangular Libration Points of the RTBP.- Nonlinear Stability Zones Around the Triangular Lagrangian Points.- An Investigation of Orbits Around the Triangular Lagrangian Points of Saturn.- Collision Orbits in the Isosceles Rectilinear Restricted Problem.- Asymptotic Orbits as Terminations of Families of Periodic Orbits in the Copenhagen Problem with and without Radiation Pressure.- A Typical Family FII of Symmetric and Periodic Orbits of Charged Particles Moving in the Plane of Motion of Two Parallel Rotating Magnetic Dipoles.- Interlude: Fractals, Chaos and Quaternions.- Five: Selected Topics in Dynamics.- Order in Chaos.- Chaos as the True Source of the Irreversiblity of Time.- Representation and Classification of Dynamical Systems.- Analytic Hamiltonian Systems, the Vicinity of a Periodic Solution.- Complex Instability.- Inverse Problems Leading to Integrable Systems.- The Observer New Method for Numerical Integration of Differential Equations in the Presence of First Integrals.- Analytical Approximations for Sitnikov's Problem.- Elementary Derivation of Hopf Type Bifurcation Formulas.- Chaotic Scattering in the Gaussian Potential.- Stochastic Motion in a Central Field with a Weak Non-Rotating Bar Perturbation.- A Note on the Canonical Character of the Stiefel-Scheifele Time Element.- Fractal Structures in Self-GravitatingCosmological Flows.- Quaternionic Generalisation of the Mandelbrot Set.- Participants and Speakers.- Author Index.