## Physics of Gravitating Systems I: Equilibrium and StabilityIt would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar and lunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields. |

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### Contents

1 | |

10 | |

6 NonJeans Instabilities | 19 |

CHAPTER I | 27 |

3 Anisotropic FireHose Instability of a Collisionless Flat Layer | 37 |

4 Derivation of IntegroDifferential Equations for Normal Modes of | 43 |

5 Symmetrical Perturbations of a Flat Layer with an Isotropic | 50 |

CHAPTER II | 78 |

6 Stability of Spherically Symmetrical Systems of General Form | 207 |

7 Discussion of the Results | 235 |

CHAPTER IV | 246 |

2 Stability of a ThreeAxial Ellipsoid and an Elliptical Disk | 265 |

3 Stability of TwoAxial Collisionless Ellipsoidal Systems | 276 |

CHAPTER XI | 285 |

Problems | 296 |

Equilibrium and Stability of Flat Gravitating Systems | 323 |

3 Nonaxial Perturbations of a Collisionless Cylinder | 97 |

4 Stability of a Cylinder with Respect to Flutelike Perturbations | 104 |

6 Comparison with Oscillations of an Incompressible Cylinder | 117 |

Problems | 125 |

Equilibrium and Stability of Collisionless Spherically Symmetrical | 136 |

2 Stability of Systems with an Isotropic Particle Velocity Distribution | 152 |

3 Stability of Systems of Gravitating Particles Moving On Circular | 164 |

Orbits | 173 |

4 Stability of Systems of Gravitating Particles Moving in Elliptical Orbits | 186 |

5 Stability of Systems with Radial Trajectories of Particles | 193 |

2 Stability of a Cold Rotating Disk | 343 |

3 Stability of a Plasma Disk with a Magnetic Field | 380 |

4 Stability of a Hot Rotating Disk | 389 |

Other Applications | 411 |

Properties of Gaseous and Stellar Disks | 428 |

Problems | 434 |

445 | |

459 | |

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angular momentum angular velocity anisotropy approximation arbitrary assumed Astron calculated Chapter characteristic equation circular orbits coefficients coincide cold disk collisionless condition considered const continuous spectrum coordinates corresponding criterion cylinder decreasing defined derived described determined dispersion equation displacement distribution function eigenfrequencies eigenfunctions ellipsoid elliptical equilibrium example expression finite fo(E formula Freeman galaxies gravitating systems homogeneous hydrodynamical incompressible infinitely thin integral equation integrals of motion investigation isotropic Jeans instability kinetic equation large-scale layer linear magnetic field mass method models modes obtain parameter particles perturbed density phase phase space plane plasma Poisson equation polynomial potential energy problem radial perturbations radius region resonance respect roots rotating disk Section short-wave similar simplest solution solved sphere spherically symmetrical spheroid spiral stability boundary stars stellar Substituting surface density taking into account theory tion Toomre trajectories uniform unperturbed values velocity dispersion wavelength zero