Higher order Lagrange-Poincar, and Hamilton-Poincar, reductions
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, 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-Poincare equations ; Lagrange-Poincare equations ; Hamilton-Poincare equations ; Yang-Mills Field ; Classical Particle ; Equations
Record created on 2012-06-12, modified on 2016-08-09