ABSTRACT
When a body (or system) is in a position (or state) of equilibrium, and is subjected to a perturbation, three cases can arise: (i) if it remains in the new, disturbed position, the equilibrium is said to be indifferent (Section 2.1); (ii) if it always returns to the old, initial position, the equilibrium is stable; and (iii) if it can get farther from the equilibrium position, that is, the perturbation increases, the equilibrium is unstable. The return to equilibrium in the case of stability, or deviation from equilibrium in the unstable case, can be monotonic or oscillatory. The words stable, indifferent, and unstable are sometimes reserved for the monotonic case (Section 2.3); the oscillatory case (Sections 2.2 and 2.4) is called damped, oscillatory, or overstable, depending on whether the amplitude of the oscillation decays, stays constant, or grows. All these six cases of motion are included in a single complex expression (Sections 2.5-2.7), which is discussed (Sections 2.8 and 2.9) for a system of arbitrary order. The existence of an equilibrium is not sufficient to ensure that it actually occurs; usually only stable equilibria are found in nature or assure the correct functioning of an engineering device, bearing in mind that perturbations are almost inevitably present. The question of existence of equilibria, and their stability, applies to various kinds of systems, for example, mechanical, electrical, chemical, and so on, both in static and in dynamic conditions.
