The chaotic pendulum

Abstract

Abstract Much of the history of physics has been characterized by the effort to understand, in great detail, increasingly smaller pieces of nature; beginning with classical particles and waves, and progressing to molecules, atoms, nuclei, and elementary particles. This trend became especially pronounced in the twentieth century with the development of sophisticated experi mental apparatus capable of probing deeply into nature’s innermost parts. Aside from the sense that one is closer to reality at the deeper levels of nature, it is plausible to assume that a clear understanding of the small pieces of nature will lead to a clear view of the large picture. The whole is presumed equal to the sum of its parts. This approach is sometimes call reductionism. More recently, in certain areas of physics, the opposite methodology has proved fruitful. New structure and organization may become evident when there is complexity, large numbers of parts, several degrees of freedom, or even just sufficient energy to make a discrete change in the system. Indeed, sometimes the whole is more than the sum of its parts. This creation of new richness of behavior often occurs in the study of processes that are pushed well beyond their equilibrium configurations. Researchers find new levels of organization, new complexity that does not seem to be obvious from a consideration of the individual parts of the process (Prigogine 1980). For example, if reactants are forced rapidly into certain chemical reactions, the resultant products may show spatial or temporal ordering (Zhabotinskii 1991). Or convective systems with large temperature gradients may exhibit new structural or dynamic organization of fluid motion. Even the motion of the humble pendulum achieves a new level of complexity if it is driven energetically at nonresonant frequencies.