  The conventional Rosenfeld-Bergmann-Dirac constrained Hamiltonian algorithm
applied to Einstein-Yang-Mills theory is shown to be equivalent to a local
gauge theoretic extension of Cartan's invariant integral approach to classical
mechanics. In addition, the Hamiltonian generators of Legendre-projectable
spacetime diffeomorphism and gauge symmetries are derived directly as vanishing
Noether charges. This leads directly to their interpretation as delivering the
correct symmetry variations of both configuration and momentum feld variables.
