Stability of Equilibrium

The equilibrium of a mechanical system is stable if after a small perturbation (displacement or push) the points of the system forever afterward differ but little from their equilibrium positions; otherwise, the equilibrium is unstable. Ordinarily with small perturbations, the points of a system in stable equilibrium will perform small oscillations around their equilibrium positions; in time the oscillations are damped by resistances, so that equilibrium is reestablished. The stability of equilibrium is defined and analyzed more rigorously in the same manner as the stability of motion. For a conservative mechanical system, the sufficient condition of the stability of equilibrium is that the potential energy of the system is minimal in the equilibrium state.