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Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions

  • François Gay-BalmazEmail author
  • Darryl D. Holm
  • Tudor S. Ratiu
Article

Abstract

Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework for Lagrangian and Hamiltonian reduction by symmetry in geometric mechanics. In particular, we obtain the reduced variational principles and the associated Poisson brackets. The special case of higher order Euler-Poincaré and Lie-Poisson reduction is also studied in detail.

Keywords

variational principle symmetry connection Poisson brackets higher order tangent bundle Lie-Poisson reduction Euler-Lagrange equations Euler-Poincaré equations Lagrange-Poincaré equations Hamilton-Poincaré equations 

Mathematical subject classification

70H50 37J15 70H25 70H30 

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Copyright information

© Springer 2011

Authors and Affiliations

  • François Gay-Balmaz
    • 1
    Email author
  • Darryl D. Holm
    • 2
  • Tudor S. Ratiu
    • 3
  1. 1.Laboratoire de Météorologie DynamiqueÉcole Normale Supérieure/CNRSParisFrance
  2. 2.Department of MathematicsImperial CollegeLondonUK
  3. 3.Section de Mathématiques and Bernoulli CenterÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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