Dynamics of Stellar Systems

ContentsPreface to the English Edition Preface to the Russian Edition Introduction 1. The Subject of Stellar Dynamics 2. A Brief Outline of the Historical Development of Stellar Dynamics 3. The Fundamentals of the Synthetic Method in Stellar Dynamics 4. The Practical Significance of Stellar Dynamics I. The Fundamental Concepts of Stellar Statistics 1. Some Properties of Univariate Distribution Functions 2. Multivariate Distribution Functions 3. Statistical Properties of Stars II. The Kinematics of Stellar Systems 1. The Macroscopic Volume Element and the Star Density Function 2. The Phase Density Function 3. The Velocity Distribution Function 4. Centroids 5. The Local Motion of the Sun in the Galaxy 6. The Velocity Ellipsoid and its Determination from Observations 7. Results of Velocity Ellipsoid Determinations and some Inferences therefrom 8. The Determination of the Actual Form of the Ellipsoidal Velocity Function 9. The Differential Field of Centroid Velocities. Helmholtz' Theorem for Stellar Systems 10. Determination of the Kinematic Parameters of the Differential Field of Centroid Velocities from the Observed Velocities of Stars IIT. The Elementary Theory of Galactic Rotation 1. General Formulae of Galactic Rotation 2. The Local Field of Centroid Velocities. Generalization of Oort's Formulae 3. Oort's Formulae for an Arbitrary Plane-parallel Motion 4. The Physical Basis of the Theory of Galactic Rotation. The Nature of the K Term 5. Determination of the Parameters of Galactic Rotation from Observation 6. Determination of the Period of Rotation and Angular Velocity of the Galaxy 7. Determination of the Mass of the Galaxy 8. The Velocity of Escape and the Phenomenon of the High-velocity Stars 9. Kinematics of Centroids in the Metagalaxy 10. The Problem of Setting up a Fundamental Coordinate System IV. Irregular Forces in Stellar Systems 1. The Fundamental Quantities which Characterize the State of a Stellar System 2. Star Encounters. Regular and Irregular Forces 3. The Effect of Irregular Forces: Individual Encounters 4. The Effect of Irregular Forces: the Cumulative Effect 5. Various Types of Equilibrium of Stellar Systems. The Quasi-steady State 6. The Relaxation Time and the Disintegration Half-life 7. The Fundamental Paradox in the Classical Dynamics of Stellar Systems 8. The Interaction of Stars with Dust Clouds 9. The Invariance of Maxwell's and Schwarzschild's Velocity Distribution Laws in Stellar Encounters V. Statistical Stellar Dynamics Neglecting Encounters 1. The Fundamental Differential Equation of Stellar Dynamics 2. The Boltzmann Equation in Curvilinear Coordinates 3. Jeans' Theorem and Liouville's Theorem 4. The Integrals of the Motion in Some Typical Cases 5. One-valued and Many-valued Integrals. The Ergodic Hypothesis in Stellar Dynamics 147 6. Jeans' Problem. The Symmetry of the Distribution in Velocity Space 7. The Inverse Jeans' Problem 8. The Importance of Using One-valued Integrals of the Motion 9. Quasi-integrals of the Motion. Oort's Quasi-integral 10. The Problem of the Third Integral for Systems with Rotational Symmetry 11. The Potential Energy of Stellar Systems 12. The Virial Theorem. Poincare's Theorem on the Limiting Angular Velocity of Rotation VI. Regular Orbits of Stars 1. Circular and Almost Circular Orbits in a Stellar System with Rotational Symmetry and a Plane of Symmetry 2. Determination of the Potential of the Galaxy 3. Some Properties of Regular Galactic Orbits 4. The Distribution of Mass in the Galaxy and Some Related Problems 5. Some Properties of Star Orbits in Spherical Systems VTT. The Problem of Local Dynamics 1. Statement of the Problem 2. The Local Cluster and its Motion in the Galaxy 3.