Collisionless Systems Equilibrium

This lecture covers the equilibrium of collisionless systems, focusing on models defined from distribution functions (DFs) such as the isothermal sphere and polytropes. It delves into anisotropic DFs in spherical systems, the Jeans Equations, and equilibria of collisionless systems. The lecture also discusses the structure of isothermal self-gravitating spheres, velocity distribution functions, and solutions of the Poisson equation. Additionally, it explores models with finite potential and density, numerical solutions of non-singular isothermal spheres, and King models with constant anisotropy. The presentation concludes with the Jeans Equations for cylindrical and axisymmetric systems, interpreting the moments and rotation curves for Miyamoto-Nagai disks.