Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 3 and August 13, 1987 under the title "Long Term Dynamical Behaviour of Natural and Artificial N-body Systems". The Institute was the latest in a series held in 1972, 1975, 1978, 1981, 1984 in dynamical astronomy, theoretical mechanics and celestial mechanics under the Directorship of Professor Victor Szebehely. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received and valuable Proceedings. In correspondence with Professor Szebehely and in long discussions with him in Colorado in August 1985, I agreed to his request that I undertake the preparation of a new ASI. I was happy to do so knowing I could call upon his vast experience in overseeing such ASI's. The last quarter century has been a period in which increasingly rapid progress has been made in celestial mechanics and related subjects not only because of the appearance of new problems urgently requiring solution but also because of the advent of new analytical techniques and powerful computer hardware and software.

Inhalt

I: Planetary Dynamics.- Dynamical Evolution of Planetary Systems and the Significance of Bode's Law.- Further Numerical Investigations into the Significance of Bode's Law.- Where are the Saturnian Trojans?.- Orbital Evolution.- Planetary Perturbation Theory from Lie Series, including Resonance and Critical Arguments.- Secular Perturbations of Planetary Orbits and their Representation as Series.- The Accumulation of Integration Error.- Numerical Regularization of the Lagrange Planetary Equations.- II: Dynamics of Natural and Artificial Satellites.- General Formulas for Three-Body Resonances.- Analytical Methods for the Radial Intermediaries.- Analytical Theory of the Rotation of an Artificial Satellite.- Some Models for the Motion of the Co-orbital Satellites of Saturn.- Long-period Changes in the Semimajor Axis of Lageos.- Effects of a Non-circular Shepherd upon a Planetary Ring.- General Motion of a Triaxial Rigid Body in a Newtonian Force Field.- The Motion of the Orbit Plane of Iapetus.- Astrodynamics in the Real-World Environment (The Whole Truth and Nothing but the Truth).- A Finite-Time Stability Criterion for Sun-perturbed Planetary Satellites.- A New Radial Intermediary and its Numerical Integration.- Co-orbital Satellites and Hill's Lunar Problem.- III: Dynamics of Asteroids.- The Puzzle of Asteroid Families.- High Eccentricity Libration.- Evolution of Asteroidal Orbits Located in the Main Secular Resonances ?5,?6 and ?16.- Algebraic Mappings Near a Resonance with an Application to Asteroid Motion.- The Hierarchical Restricted Problem with Applications.- The Motions of Asteroids in the Secular Resonance ?6: an Analytical Model and Numerical Calculations.- IV: Dynamics of Stars and Galaxies.- Families of Periodic Orbits in a Model of Interacting Galaxies.- Qualitative Characteristics of Dynamical Systems.- On the Galactic Motion.- The N-Body Problem in Stellar Dynamics.- Rotationally and Tidally Perturbed Orbital Elements of Close Binary Stars.- V: Other Specific Topics in Dynamics.- Escape and Capture in the Restricted Three Body Problem (RTBP).- A Formulation of the N-body Problem where the Velocities are Bounded.- A Report on Some New KAM Estimates.- Extended Canonical Transformations Increasing the Number of Variables.- Non Local Spiraling Characteristic Curves.- Connectance and Stability of Linear Differential Systems.- Resonances in the Planar Elliptic Restricted Problem.- The Near-Resonance Theorem: Analysis of the Vicinity of Periodic Solutions of Analytic Differential Systems.- Homoclinic and Heteroclinic Solutions of the RTBP Joining the Triangular Equilibrium Points.- Double Collision Orbits and Second Species Solutions in the Restricted Three-Body Problem.- Bifurcations and Instabilities in the Restricted Three-Body Problem.- Three Dimensional Equations of Szebehely of the Inverse Problem and Frenet Reference Frame.- Fourier Transform in Astrodynamics.- Estimates of the Error in Normal Forms of Hamiltonian Systems. Applications to Effective Stability and Examples.- Passages Near Triple Collision.- Non-Integrability of Hamiltonian Systems Based on Ziglin's Theorem.- Index of Names.- Index of Subjects.