9 - Applications of chaos

Summary

In this chapter we briefly present how chaos appears in problems of a larger scale. We wish to illustrate by this (i) the ubiquity of chaos and (ii) that numerous research problems are still to be resolved. According to the introductory nature of this book, the selection is based on cases that are not too technically complicated. Solved problems are not provided in this chapter; we merely formulate questions that may encourage the reader to investigate the subject further. We emphasise that, for a given phenomenon, different aspects of chaos (permanent–transient, dissipative–conservative) may be present simultaneously.

We start our survey with two problems, one related to space research, the other to engineering practice, that have also played historically important roles: the gravitational three-body problem and the dynamics of a heavy asymmetric top. Next we turn to a simple model of the general atmospheric circulation, which nevertheless reflects important features of the weather. Finally, we overview the occurrence of chaotic behaviour related to fluid flows, and, in connection with this, we point out the relevance of chaotic mixing in environmental fluid flows. Further fields of application are discussed in the Boxes in this chapter.

Spacecraft and planets: the three-body problem

In the course of their motion, spacecraft are subject to the gravitational attraction of neighbouring celestial bodies. As gravitational interaction with the Earth decays slowly, the effect of at least two celestial bodies on the spacecraft have to be taken into account; i.e., that of the Earth–Moon, or (if the spacecraft moves further away) that of the Sun–Jupiter couple.