Peter E. Crouch
In collaboration with Antohy M. Bloch, Darryl D. Holm, Jerrold
E. Marsden, Tudor S. Ratiu
College of Engineering and Applied Sciences
Arizona State University
A comparison of the rgid body equations and the incompressible, inviscid ideal fluid flow equations, with the extremals of two optimal control problems
In this talk, we describe two dynamical systems, related to the generalized rigid body equations and the incompressible, inviscid fluid flow equations, that are obtained as the extremal flows of two optimal control problems. We then discuss the relations between these extremal flows and the classical systems. These relations yield new insights into the classical systems, including seemingly new Hamiltonian represtations for both systems. If there is time, the Moser-Veselov discretization of the rigid body equations will be derived from a corresponding optimal control problem, exhibiting the same structureas the continuous time analog.