The Clebsch Representation in Optimal Control and Low Rank Integrable Systems

  • Anthony M. BlochEmail author
  • François Gay-Balmaz
  • Tudor S. Ratiu
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)


Certain kinematic optimal control problems (the Clebsch problems) and their connection to classical integrable systems are considered. In particular, the rigid body problem and its rank 2k counterparts, the geodesic flows on Stiefel manifolds and their connection with the work of Moser, flows on symmetric matrices, and the Toda flows are studied.



AMB was partially supported by NSF grants DMS-1613819, AFSOR grant 9550-18-0028, INSPIRE 1343720 and the Simons Foundation. FGB was partially supported by ANR grant GEOMFLUID 14-CE23-0002-01. TSR was partially supported by National Natural Science Foundation of China grant number 11871334 and by Swiss NSF grant NCCR SwissMAP. We thank the referees for their useful comments.


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Authors and Affiliations

  • Anthony M. Bloch
    • 1
  • François Gay-Balmaz
    • 2
  • Tudor S. Ratiu
    • 3
    • 4
    • 5
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.CNRS – LMD – IPSL, Ecole Normale SupérieureParisFrance
  3. 3.School of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  4. 4.Section de MathématiquesUniversité de GenéveGenéveSwitzerland
  5. 5.École Polytechnique Fédérale de LausanneLausanneSwitzerland

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