Higher order Lagrange-Poincar\'e and Hamilton-Poincar\'e reductions
Mathematical Physics
2014-07-02 v1 math.MP
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-Poincar\'e and Lie-Poisson reduction is also studied in detail.
Cite
@article{arxiv.1407.0273,
title = {Higher order Lagrange-Poincar\'e and Hamilton-Poincar\'e reductions},
author = {François Gay-Balmaz and Darryl D. Holm and Tudor S. Ratiu},
journal= {arXiv preprint arXiv:1407.0273},
year = {2014}
}
Comments
This paper has appeared in 2011 in the Journal of the Brazilian Mathematical Society 42(4), 579--606