The overwhelming thrust in undergraduate and graduate teaching in science and engineering is to seek, describe and design order in physical systems. Perhaps the paradigm of celestial mechanics and the prediction of the movement of the heavenly bodies, based on Newton's laws, is a good example of a 'clockwork' image of the world.
However, the emergence of nonlinear dynamics and chaos has shed light on the inherent disorder present even in relatively simple mathematical and physical models. Significant and fundamental research in this field poses some deep questions on the complexity and predictability of time-evolving physical systems. This is in marked contrast to the rather simplistic view based, for example, on the traditional linear theory of ordinary differential equations. Most real physical systems are nonlinear.
An effective means of conveying these ideas (together with familiar linear behavior) is achieved using mechanical experiments. A cart rolling on a curved surface can be made to mimic linear or nonlinear dynamic behavior depending on the shape of the track, e.g. a locally concave, parabolic surface corresponds to the potential energy associated with a linear spring obeying Hooke's law. Deviations from this parabola corresponds to nonlinearity in stiffness. Both free and forced responses are observed together with a clear demonstration of chaos.
These demonstrations highlight our ability, or inability, to predict the future behavior of certain physical systems even in cases where we have an accurate mathematical model. More practical applications of nonlinear dynamics ranges from the small scale oscillations of a pendulum to the large scale motion leading to the capsize of ships, as well as many examples drawn from the breadth of science and engineering.
Within this cluster of web pages, you can meet the members of the Nonlinear Dynamics Research Group and read about their current research projects. After that take a visual tour of the group's research facilities. The group has hosted a couple of workshops on Nonlinear Dynamics:
Note: A workshop on "Exploiting Nonlinear Dynamics" was held at the International Center for Mechnaical Sciences (CISM) in Udine, Italy, in September, 2010. Please click here for more details. A book manuscript of the lectures will be available in late 2011.