Collisionless Systems: Equilibria & Models

This lecture covers the collisionless Boltzmann equation, self-consistent spherical models, Jeans theorems, and DFs from mass distribution. It explores the Eddington formula, isotropic and isothermal models, and the relation between DFs and velocity moments. The lecture also delves into the symmetries and properties of collisionless systems, such as spherical, cylindrical, and Cartesian coordinates. Various DFs are discussed, including ergodic and symmetrical ones, along with velocity dispersions and their implications. The presentation concludes with examples of power law models and analytical solutions for different scenarios.