Variational Integrators for Degenerate Lagrangians, with Application to Point Vortices
Rowley, C. W. and J. E. Marsden
Proceedings of the 41st IEEE Conference on Decision and Control, 1521-1527.
Abstract:
We develop discrete mechanics and variational integrators for a class
of degenerate Lagrangian systems, and apply these integrators to a system
of point vortices. Excellent numerical behavior is observed. A longer term
goal is to use these integration methods in the context of control of mechanical
systems, such as coordinated groups of underwater vehicles. In fact, numerical
evidence given in related problems shows that in the presence of external forces,
these methods give superior predictions of energy behavior.
