  Based on the insight gained by many authors over the years on the structure
of the Einstein-Hilbert, Gauss-Bonnet and Lovelock gravity Lagrangians, we show
how to derive -- in an elementary fashion -- their first-order, generalized
"ADM" Lagrangian and associated Hamiltonian. To do so, we start from the
Lovelock Lagrangian supplemented with the Myers boundary term, which guarantees
a Dirichlet variational principle with a surface term of the form
$\pi^{ij}\delta h_{ij}$, where $\pi^{ij}$ is the canonical momentum conjugate
to the boundary metric $h_{ij}$. Then, the first-order Lagrangian density is
obtained either by integration of $\pi^{ij}$ over the metric derivative
$\partial_wh_{ij}$ normal to the boundary, or by rewriting the Myers term as a
bulk term.
