Gay-Balmaz, FrancoisRatiu, Tudor S.2011-12-162011-12-162011-12-16201110.3934/jgm.2011.3.41https://infoscience.epfl.ch/handle/20.500.14299/74097WOS:000290655400003This 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.Optimal controlClebsch variablesmomentum mapEuler-Poincare equationdouble bracket equationEuler equationnormal metricgeodesicSemidirect ProductsGeodesic-FlowsFluidsReductionManifoldsEquationsSymmetrytext::journal::journal article::research article