ABSTRACT
The eminent eighteenth century astronomer and mathematician Pierre Simon de Laplace was a great believer in the predictability of motion. However, in the late 1980s, Gerald Sussman, Jack Wisdom and colleagues at the Massachusetts Institute of Technology made a digital orrery: a specialized computer designed to calculate the paths of the planets over extremely long periods of time. Tiny differences in initial conditions eventually produce huge differences in the subsequent position, to such an extent that the word ‘predictable’ becomes quite inappropriate. This unpredictability in the motion of the planets is an example of chaos, or chaotic motion. The chaotic behaviour is inherent in the equations of celestial mechanics that predict the motion of the planets. This chapter begins the study of chaos by looking at some deterministic systems that are much simpler than those encountered in celestial mechanics.
