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.
| Original language | English |
|---|---|
| Pages (from-to) | 579-606 |
| Number of pages | 28 |
| Journal | Bulletin of the Brazilian Mathematical Society |
| Volume | 42 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Jan 2011 |
Keywords
- Euler-Lagrange equations
- Euler-Poincaré equations
- Hamilton-Poincaré equations
- Lagrange-Poincaré equations
- Lie-Poisson reduction
- Poisson brackets
- connection
- higher order tangent bundle
- symmetry
- variational principle
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