This volume contains the proceedings of the third IAU conference on the Gravita tional N-Body Problem. The first IAU conference [IJ, six years ago, was motivated by the renaissance in Celestial Mechanics following the launching of artificial earth satellites, and was an attempt to bring to bear on the problems of Stellar Dynamics the sophisticated analytical techniques of Celestial Mechanics. That meeting was an outgrowth of the 'Summer Institutes in Celestial Mechanics' initiated by Dirk Brouwer. By the second IAU conference [2J, our interest had been captured by the attempts to simulate stellar systems on the computer. Computer simulation is now an essential part of stellar dynamics; journals of computational physics have started in the United Kingdom and in the United States and symposia on computer simulation of many-body problems have become a perennial event [3,4, 5]. Although our early hopes that the computer would 'solve' our problem have been tempered by experience, some techniques of computer simulation have now matured through five years of testing and use. A working description of the six most popular methods is appended to this volume. During the past three years, stellar dynamicists have followed closely the develop ments in the related field of Plasma Physics. The contexts of Plasma and Stellar Physics are deceptively similar; at first, results from Plasma Physics were bodily transferred to stellar systems by 'changing the sign of the coupling'. We are more sophisticated and more skeptical now.

Proceedings of IAU Colloquium No. 10, held at the Institute of Theoretical Astronomy, Cambridge University, Cambridge, August 12-15, 1970

Inhalt
I / Collisional Systems.- A. Analytic Treatments.- Collisional Processes in Stellar Systems.- Polarization Clouds and Dynamical Friction.- A Certain Discontinuous Markov Process in Stellar Dynamics.- Relaxation Times in Strictly Disk Systems.- B. Numerical Experiments.- Numerical Experiments on the N-Body Problem.- Monte Carlo Models of Star Clusters.- A Fluid-Dynamical Method for Computing the Evolution of Star Clusters.- On the Lifetimes of Galactic Clusters.- Disruption of Star Clusters through Passing Interstellar Clouds Investigated by Numerical Experiments.- Numerical Experiments on the Escape from Non-Isolated Clusters and the Formation of Multiple Stars.- Binary Evolution in Stellar Systems.- On the Dissolution Time of a Class of Binary Systems.- On the Reproducibility of Run-Away Stars Formed in Collapsing Clusters.- Numerical Experiments on Pair Correlations and on 'Thermodynamics'.- A Numerical Experiment on Relaxation Times in Stellar Dynamics.- Recent Developments of Integrating the Gravitational Problem of N-Bodies.- A Multi-Particle Regularisation Technique.- The Use of Integrals in Numerical Integrations of the N-Body Problem.- II / Collisionless Systems.- A. Analytic Treatments.- Collisionless Stellar Dynamics.- On the Origin and Permanence of Galactic Spirals.- The Hose-Pipe Instability in Stellar Systems.- On the Stability of an Encounterless Self-Gravitating Constant Density System.- Exact Statistical Mechanics of a One-Dimensional Self-Gravitating System.- B. Numerical Experiments.- Numerical Experiments in Collisionless Systems.- Dynamics of Plane Stellar Systems.- Numerical Experiments in Spiral Structure.- On the Number of Isolating Integrals in Systems with Three Degrees of Freedom.- Numerical Experiments on Lynden-Bell's Statistics.- A Phase-Space Boundary Integration of the Vlasov Equation for Collisionless One-Dimensional Stellar Systems.- The Collective Relaxation of Two-Phase-Space-Density Collisionless One-Dimensional Selfgravitating Systems.- Numerical Experiments with a One-Dimensonal Gravitational System by an Euler-Type Method (Summary).- N-Body Problem and Gas Dynamics in One Dimension (Abstract).- III / Numerical Experiments and Analytical Treatments in Plasma Physics.- Computer Simulation of Plasmas.- Enhancement of Relaxation Processes by Collective Effects.- Stability Properties for Encounterless Self-Gravitational Stellar Gas and Plasma.- IV / Summary of the Colloquium.- V / Appendix: Methods of Computer Simulation of the Gravitational N-Body Problem.- Direct Integration Methods of the N-Body Problem.- Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N Bodies.- The Monte Carlo Method.- The Fluid-Dynamical Method.- The Model of Spherical Concentric Shells.- Integration Methods where Force is Obtained from the Smoothed Gravitational Field.