From Newton to Chaos

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.