Mechanics: Equilibrium Points and Stability

This lecture covers the concept of equilibrium points in mechanical systems, defined as the solutions of the equations of motion when the generalized coordinates have zero derivatives. Stability of equilibrium points is discussed, where a stable point tends to return to its position after a disturbance, while an unstable point moves away. Examples like the simple pendulum and a sliding bead on different surfaces are used to illustrate these concepts. The lecture also delves into the analysis of stability by applying small perturbations around equilibrium points and determining their effects. Various forces and constraints are considered to understand the dynamics of systems in equilibrium.