# Higher order Lagrange-Poincaré and Hamilton-Poincaré reductions

@article{GayBalmaz2011HigherOL, title={Higher order Lagrange-Poincar{\'e} and Hamilton-Poincar{\'e} reductions}, author={François Gay‐Balmaz and Darryl D. Holm and Tudor S. Ratiu}, journal={Bulletin of the Brazilian Mathematical Society, New Series}, year={2011}, volume={42}, pages={579-606} }

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.

## 34 Citations

### Higher-order Variational Calculus on Lie algebroids

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### Invariant Higher-Order Variational Problems

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### Invariant Higher-Order Variational Problems

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- 2012

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We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the…

### Geometric integrators for higher-order mechanics on Lie groups

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### Matched Higher Order Lagrangian Dynamics

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New variational integrators for higher-order Lagrangian mechanical system subjected to higher- order constraints are derived from the discretization of the variational principles, showing that their methods are automatically symplectic and, in consequence, with a very good energy behavior.

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