Clebsch Optimal Control Formulation In Mechanics
This paper introduces and studies a class of optimal control problems based on the Clebsch approach to Euler-Poincare dynamics. This approach unifies and generalizes a wide range of examples appearing in the literature: the symmetric formulation of N-dimensional rigid body and its generalization to other matrix groups; optimal control for ideal flow using the back-to-labels map; the double bracket equations associated to symmetric spaces. New examples are provided such as the optimal control formulation for the N-Camassa-Holm equation and a new geodesic interpretation of its singular solutions.
Keywords: Optimal control ; Clebsch variables ; momentum map ; Euler-Poincare equation ; double bracket equation ; Euler equation ; normal metric ; geodesic ; Semidirect Products ; Geodesic-Flows ; Fluids ; Reduction ; Manifolds ; Equations ; Symmetry
Record created on 2011-12-16, modified on 2016-08-09