Reduction of Hamilton's variational principle

Abstract

This paper builds on the initial work of Marsden and Scheurle on nonabelian Routh reduction. The main objective is to carry out the reduction of variational principles in further detail. In particular, we obtain reduced variational principles which are the symplectic analogue of the well-known reduced variational principles for the Euler-Poincare equations and the Lagrange-Poincare equations. On the Lagrangian side, the symplectic analogue is obtained by suitably imposing the constraints of preservation of the momentum map.