Gauged Lie-Poisson structures
Montgomery, R., J. E. Marsden, and T. Ratiu
Contemp. Math., 28, 101-114
Abstract:
A global formula for Poisson brackets on reduced cotangent bundles of principal bundles is derived. The result bears on the basic constructions for interacting systems due to Sternberg and Weinstein and on Poisson brackets involving semi-direct products for fluid and plasma systems. The formula involves Lie-Poisson structures, canonical brackets, and curvature terms.
