Nonlinear science has a broad range of applications in vehicle dynamics and
other fields of engineering ranging from the damping of vibrating machines
and the stabilization of lasers and chemical reactors to the maneuvering of
aircrafts in the post stall regime where conventional controls become
inefficient because of detaching airflows. Other problems of aircraft
dynamics relate to the sensitivity of spin entry and spin recovery maneuvers
to an offset of the lateral center of mass of the aircraft and to the
gyroscopic torque from the rotors of the engines.
On the background of a recent prediction of 70% growth in the total transport volume in the EU before year 2010, revitalization of the railways as a preferred mode of transportation represents a promising alternative. However, the quality of railway transport must be improved, and the speed must be increased. This involves the development of new types of suspense systems that can provide a smoother ride while at the same time reducing noise and wear of the tracks.
Other applications relate to the prevention of catastrophies at sea. Situations may actually arise that a boat capsizes even though the design and stability conform with all required standards. The problem is that the ship may be linearly stable, but globally unstable in the sense that it capsizes under large amplitude rolling or swaying motions. Moreover, the basin of attraction for the linearly stable state may completely erode. Many technical control systems operate with on-off regulation and hence have no stable equilibrium points.
For households installations this is the case, for instance, for refrigerators and freezers as well as for air conditioners and oil and gas burners. In the construction of industrial plants, engineers similarly exploit the simplicity and robustness of on-off regulation for a variety of different functions. Interaction between two such systems can lead to a broad range of complex nonlinear dynamic phenomena, including mode-locking, period-doubling bifurcations, chaos, and coexisting solutions with fractal basin boundaries.
Research is presently concentrated on