Variational integrators for degenerate Lagrangians, with application to point vortices

C. W. Rowley and J. E. Marsden

Proceedings of the 41st IEEE CDC , December 2002.


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, such as those in Kane et al. (Int. J. Num. Math. Eng. 49, 2000) shows that in the presence of external forces, these methods give superior predictions of energy behavior.

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