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research article

Clebsch Optimal Control Formulation In Mechanics

Gay-Balmaz, Francois  
•
Ratiu, Tudor S.  
2011
Journal Of Geometric 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.

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Type
research article
DOI
10.3934/jgm.2011.3.41
Web of Science ID

WOS:000290655400003

Author(s)
Gay-Balmaz, Francois  
Ratiu, Tudor S.  
Date Issued

2011

Published in
Journal Of Geometric Mechanics
Volume

3

Start page

41

End page

79

Subjects

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

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
CAG2  
Available on Infoscience
December 16, 2011
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/74097
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