ix List of Speakers and Participants xi Group Photograph xviii Greetings by B. Garfinkel, A. E. Roy and P. J. Message xix Introduction xxiii PART I: FUNDAMENTAL CONSIDERATIONS OF STABILITY R. BROUCKE/Simple Non-Integrable Systems with Two Degrees of Freedom 3 G. CONTOPOULOS/lnstabilities in Systems of Three Degrees of Freedom 25 R. W. EASTON/Perturbed Twist Maps, Homoclinic Points and Ergodic Zones 41 O. GUREL/Bifurcation Theory and its Applications V. SZEBEHELY/General Considerations of Stability in 49 61 Celestial Mechanics PART II: ASPECTS OF NUMERICAL ANALYSIS AND STATISTICAL MECHANICS S. J. AARSETH/An N-Body Integration Method in Co-Moving Coordinates 69 J. BAUMGARTE/The General Theory of Conservative Stabilization of the Keplerian Problem 81 C. DEWITT-MORETTE /Celestial Mechanics, Quantum Mechanics, and Path Integration 95 G. C. STEY/Statistical Viewpoint in Classical Mechanics 103 PART III: STABILITY OF PLANETARY SYSTEMS ~ C. FROESCHLE and H. SCHOLL/Evolution of Orbits in the Outer Part of the Asteroidal Belt and in the Kirkwood Gaps as Influenced by the Mass Effects of Saturn and Jupiter 115 v TABLE OF CONTENTS vi B. GARFINKEL/On the Stability of Resonant Motion in 121 the Light of the Regularizing Function 129 P. GOLDREICH/The Rings of Saturn and Uranus J. D. HADJIDEMETRIOU/Instabilities in Periodic 135 Planetary-Type Orbits P. J. MESSAGE/Bounds on Secular Terms in Celestial 165 Mechanics A. E. ROY/Empirical Stability Criteria in the 177 Many-Body Problem R. O. VICENTE/Instabilities in Planetary Systems 211 PART IV: THE PROBLEM OF THREE BODIES H.

Proceedings of the NATO Advanced Study Institute, Cortina D'Ampezzo, Italy, July 30-August 12, 1978

Inhalt
I: Fundamental Considerations of Stability.- Simple Non-Integrable Systems with Two Degrees of Freedom.- Instabilities in Systems of Three Degrees of Freedom.- Perturbed Twist Maps, Homoclinic Points and Ergodic Zones.- Bifurcation Theory and its Applications.- General Considerations of Stability in Celestial Mechanics.- II: Aspects of Numerical Analysis and Statistical Mechanics.- An N-Body Integration Method in Co-Moving Coordinates.- The General Theory of Conservative Stabilization of the Keplerian Problem.- Celestial Mechanics, Quantum Mechanics, and Path Integration.- Statistical Viewpoint in Classical Mechanics.- III: Stability of Planetary Systems.- Evolution of Orbits in the Outer Part of the Asteroidal Belt and in the Kirkwood Gaps as Influenced by the Mass Effects of Saturn and Jupiter.- On the Stability of Resonant Motion in the Light of the Regularizing function.- The Rings of Saturn and Uranus.- Instabilities in Periodic Planetary-Type Orbits.- Bounds on Secular Terms in Celestial Mechanics.- Empirical Stability Criteria in the Many-Body Problem.- Instabilities in Planetary Systems.- IV: The Problem of Three Bodies.- Note on the Triangular Lagrangian Points in the Elliptic Restricted Problem of Three Bodies.- Periodic Orbits with and without Symmetry in the Three-Dimensional General Three-Body Problem.- The Vicinity of the Primary of Small Mass in the Restricted Problem.- Stab1e and Unstable Manifolds in Planar Triple Collision.- V: Abstracts of Seminar-Contributions.- Cluster Formation and Gravitational Instabilities.- Application of a New Numerical Method for the Integration of the Equations of Motion for an N-Body System.- Evolution of a Mission Concept from a Solar Probe to a Solar Orbiter.- Simulation of Dynamical and Thermal Behaviour of Skyhook System.- The Jacobian Integral in the Elliptic Restricted Three-Body Problem.- Effect of Mass-Parameter on the Periodic Orbits of the Restricted Problem of Three Bodies.- Semi-Analytical Lunar Ephemeris.- On the Origin of the Kirkwood Gaps.- Generating Orbits for Stable Close Encounter Periodic Solutions of the Restricted Problem.- Optimal Continuous Torque Attitude Maneuvers.- Final Evolutions of Parabolic-Hyperbolic Type in the Restricted Three-Body Problem.- Asymptotic Orbits and Instability Zones in the Simplest Model of a Galactic Potential.- Generation of Periodic Orbits in the Three-Body Problem.- Measurement of the Gravitational Constant in Space.- Hill's Stability Applied to the Asteroidal Belt.- Numerical Study of the Rectilinear Isosceles Restricted Problem.- Analytical Construction of Unstable Periodic Orbits about the Collinear Points.- On the Stability of an Equilibrium Solution in Hamiltonian Systems of Two Degrees of Freedom.- Regularization of Triple Collisions in the General Three-Body Problem.- Index of Names.- Index of Subjects.