This course describes the physics of collisionless, gravitational N-body systems (stellar systems and dark matter halos). Topics covered include potential theory, orbit theory, collisionless Boltzmann equation, Jeans equations, disk stability, violent relaxation, phase mixing, dynamical friction and kinetic theory.  The lecture notes below are part of the course I tought in 2005 at the ETH in Zurich.

These are the lecture notes of a course I have given in 2005 at ETH, Zurich.
  • Lecture 1:  Vector Calculus, Integral Theorems, Curvi-Linear Coordinate Systems, Newton’s Laws, Self-Consistency Problem, Timescales
  • Lecture 2: Potential Theory, Poisson Equation, Spherical Systems, Ellipsoidal Systems, Multipole Expansion, Disk Potentials
  • Lecture 3: Lagrangian & Hamiltonian formalism, Noether’s Theorem, Poisson Brackets, Canonical Transformations, Hamilton-Jacobi Equation
  • Lecture 4: Integrals of Motion, Action-Angle variables, Near-Integrable Systems, KAM Theorem
  • Lecture 5: Surfaces of Section, Orbits in Spherical Potentials, Orbits in Planar Potentials
  • Lecture 6: Orbits in Axisymmetric Potentials, Epicycle Approximation, Orbits in Triaxial Potentials, Rotating Potentials, Lindblad Resonances
  • Lecture 7: Distribution Functions (Coarse-grained vs. Fine-grained), Collisionless Boltzmann Equation, Jeans Equations
  • Lecture 8: Virial Equations and Applications, Jeans Theorem, Spherical Models, Mass-Anisotropy Degeneracy
  • Lecture 9: Axisymmetric Models (Two-Integral Jeans models and Three-Integral Schwarzschild models), Triaxial Systems
  • Lecture 10:Kinematics, Relaxation & Virialization, Phase Mixing, Chaotic Mixing, Violent Relaxation, Landau Damping
  • Lecture 11: Collisions between Collisionless Systems, Dynamical Friction, Orbital Decay, Impulse Approximation, Gravothermal Catastrophe



Here are a number of excellent textbooks that cover this material in detail:

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