In the engineered world (and in a good deal of the natural world), stable equilibrium, or some kind of stationary or steady-state behavior, is the order of the day. Systems are designed to operate in a predictable fashion to fulfill their intended functions despite disturbances and changing conditions. Control systems have been spectacularly successful in maintaining a desirable (stable) response given inevitable uncertainty in modeling system physics. However, there are plenty of examples of systems becoming unstable - and often the consequences of instability are severe. This book looks at the interplay between vibrations and stability in elastic structures.

A brief view of an ecological system provides an effective analogy. The competition between certain species can be viewed as a coupled dynamic system in a slowly changing environment. External influences are provided by various factors including the climate, disease, and human influence. The delicate interaction is played out as conditions evolve and populations respond accordingly - usually in a correspondingly slow way also. However, an instability may occur leading to extinction on a relatively short time scale, perhaps when a disease (or massive meteorite) wipes out an entire population. This situation is not that dissimilar to the fluctuations of the stock markets (in which prediction of changes is of concern to individuals and governments).