The Concept of Stability and Types of Instability THE term stable or unstable is applied to a body or system in accordance with the nature of the ultimate consequence of applying a disturbance. If the body or system is at rest and in equilibrium in a certain configuration, that configuration is said to be completely stable if the system ultimately comes to rest in the same configuration after the imposition of any disturbance. Frequently interest is confined to small disturbances the term small is vague but must be interpreted as meaning that the motions of disturbance or deviations are so bounded that they can be described by linear differential equations. When this is so, the investigation of the stability becomes relatively easy and the actual magnitudes of the initial disturbances are not required in the discussion of the stability. The same concept of stability for small disturbances can obviously be applied to any steady motion and indeed to any regular motion. The criterion for stability is that the deviations from the basic motion consequent upon a small disturbance shall ultimately become vanishingly small.
Aircraft Engineering and Aerospace Technology – Emerald Publishing
Published: Feb 1, 1945