TABLE OF CONTENTS The stability of rigid bodies is illustrated clearly by the well-known example of a ball on curved planes (Fig. 3.1). Resting on a concave surface it is stable [Fig. 3.1(a)]. resting on a convex surface it is unstable [Fig. 3.1(b)], and on a horizontal surface it is in neutral equilibrium [Fig. 3.1(c)]. The terminology stable or unstable ordinarily refers to small disturbances from the equilibrium position. A large disturbance can throw the ball into an unstable region, but the equilibrium configuration (a) generally would be accepted as stable. On the other hand an extremely small flat region at the ball contact point also will make for stability in the small and not in the large but equilibrium configuration (b) still would be thought of as unstable.
Stability of such static systems may be defined in several equivalent ways. The usual concept of stability of a static equilibrium system can be defined by observing the relationship between small disturbing input and resulting displacement output. The system is stable if the displacement output of the system is small for all permissible added disturbances. On the other hand, if the resulting displacement output of the system is large in comparison with the magnitude of the input, the system is unstable. In case of a structure, the disturbing input may be a set of load or displacements and the resulting output is usually deformations or displacements. Stability condition in these cases may be checked by deforming...
