  We investigate G-invariant symplectic structures on the cotangent bundle T*P
of a principal G-bundle P(M,G) which are canonically related to automorphisms
of the tangent bundle TP covering the identity map of P and commuting with the
action of TG on TP. The symplectic structures corresponding to connections on
P(M,G) are also investigated. The Marsden-Weinstein reduction procedure for
these symplectic structures is discussed.
