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(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- VII Problems of Nonlinear Theory.- II Astrophysical Applications.- VIII General Remarks.- IX Spherical Systems.- X Ellipsoidal Systems.- XI Disk-like Systems. Spiral Structure.- XII Other Applications.- 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. "Lagrange" Derivation of the Matrix Equation.- 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- 11. Derivation of the Kinetic Equation for Waves.- 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.tion of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- 5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- 1. Oort's Antievolutionary Hypothesis.- 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- 4. Lynden-Bell's Collisionless Relaxation.- 5. Estimates of "Collisionlessness" of Particles in Different Real Systems.- IX Spherical Systems.- 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- 2. Classification of Unstable Modes in Scales.- 3. Universal Criterion of the Instability.- 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System's Evolution.- 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- 6. Example of Strongly Unstable Model.- 7. Can Lynden-Bell's Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- 8. Is the "Unstable" Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a "Black Hole"?.- X Ellipsoidal Systems.- 1. Objects Under Study.- 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- 3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- 1. Different Points of View on the Nature of Spiral Structure.- 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The
Contents
(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- VII Problems of Nonlinear Theory.- II Astrophysical Applications.- VIII General Remarks.- IX Spherical Systems.- X Ellipsoidal Systems.- XI Disk-like Systems. Spiral Structure.- XII Other Applications.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. "Lagrange" Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.
