Preface xiii Chapter 1. Introduction 1 1.1 An overview of the observations 5 1.2 Collisionless systems and the relaxation time 33 The relaxation time 34 1.3 The cosmological context 37 Chapter 2. Potential Theory 55 2.1 General results 56 The potential-energy tensor 59 2.2 Spherical systems 60 2.3 Potential-density pairs for attened systems 72 2.4 Multipole expansion 78 2.5 The potentials of spheroidal and ellipsoidal systems 83 2.6 The potentials of disks 96 2.7 The potential of our Galaxy 110 2.8 Potentials from functional expansions 118 2.9 Poisson solvers for N-body codes 122 Chapter 3. The Orbits of Stars 142 3.1 Orbits in static spherical potentials 143 3.2 Orbits in axisymmetric potentials 159 3.3 Orbits in planar non-axisymmetric potentials 171 3.4 Numerical orbit integration 196 3.5 Angle-action variables 211 3.6 Slowly varying potentials 237 3.7 Perturbations and chaos 243 3.8 Orbits in elliptical galaxies 262 Chapter 4. Equilibria of Collisionless Systems 274 4.1 The collisionless Boltzmann equation 275 4.2 Jeans theorems 283 4.3 DFs for spherical systems 287 4.4 DFs for axisymmetric density distributions 312 4.5 DFs for razor-thin disks 329 4.6 Using actions as arguments of the DF 333 4.7 Particle-based and orbit-based models 338 4.8 The Jeans and virial equations 347 4.9 Stellar kinematics as a mass detector 365 4.10 The choice of equilibrium 376 Chapter 5. Stability of Collisionless Systems 394 5.1 Introduction 394 5.2 The response of homogeneous systems 401 5.3 General theory of the response of stellar systems 417 5.4 The energy principle and secular stability 423 5.5 The response of spherical systems 432 5.6 The stability of uniformly rotating systems 439 Chapter 6. Disk Dynamics and Spiral Structure 456 6.1 Fundamentals of spiral structure 458 6.2 Wave mechanics of differentially rotating disks 481 6.3 Global stability of differentially rotating disks 505 6.4 Damping and excitation of spiral structure 518 6.5 Bars 528 6.6 Warping and buckling of disks 539 Chapter 7. Kinetic Theory 554 7.1 Relaxation processes 555 7.2 General results 559 7.3 The thermodynamics of self-gravitating systems 567 7.4 The Fokker Planck approximation 573 7.5 The evolution of spherical stellar systems 596 7.6 Summary 633 Chapter 8. Collisions and Encounters of Stellar Systems 639 8.1 Dynamical friction 643 8.2 High-speed encounters 655 8.3 Tides 674 8.4 Encounters in stellar disks 685 8.5 Mergers 695 Chapter 9. Galaxy Formation 716 9.1 Linear structure formation 717 9.2 Nonlinear structure formation 733 9.3 N-body simulations of clustering 751 9.4 Star formation and feedback 760 9.5 Conclusions 765 Appendices A. Useful numbers 770 B. Mathematical background 771 C. Special functions 785 D. Mechanics 792 E. Delaunay variables for Kepler orbits 805 F. Fluid mechanics 807 G. Discrete Fourier transforms 818 H. The Antonov Lebovitz theorem 822 I. The Doremus Feix Baumann theorem 823 J. Angular-momentum transport in disks 825 K. Derivation of the reduction factor 830 L. The diffusion coefficients 833 M. The distribution of binary energies 838 References 842 Index 857