Collisionless Systems Stability

This lecture covers the stability of collisionless systems, focusing on the Virial Equation, Equilibria, and Moments of the Collisionless Boltzmann Equation. It explores the applications of the Virial Theorem, N-body experiments, and the interpretation of the Euler equation in hydrodynamics. The lecture delves into the definitions of symmetric kinetic energy tensors, potential energy tensors, and inertial tensors, emphasizing ordered and random motions. It discusses the Plummer model, Jeans equations for spherical systems, and the Miyamoto-Nagai disk model. The instructor also analyzes the origin of instability in systems, considering symmetry breaks, uncoupled motions, and anisotropies in velocity dispersions.