Lecture
This lecture covers the stability of Lagrange points in the context of celestial mechanics, focusing on the equilibrium points in the rotating frame of reference where the masses of celestial bodies are fixed. Analytical calculations and numerical simulations are used to study the effects of inertia, centrifugal force, and the Coriolis effect on the movement of celestial bodies. The lecture also explores the concept of Lagrange points, reduced problems like 'planet x', and the dynamics of a third celestial body in the system. Various equations of motion for the third body in different reference frames are analyzed, along with the significance of Lagrange points in the stability of celestial systems.