Lecture
This lecture explores the stability of uniformly rotating systems, focusing on the spiral structures in rotating disks. It delves into the dispersion relation for fluid disks, the origin of spiral structures, and the stability against collisionless systems. The instructor discusses the response of the system to weather perturbations, solutions for stabilizing rotating systems, and the winding problem in observed spirals. Various aspects of spiral galaxies, including their shape functions and pitch angles, are also covered. The lecture concludes with a detailed analysis of the Jeans instability, the stabilizing effects of shearing motions, and the prediction of the number of spiral arms in rotating disks.