  The canonical Hamiltonian $H_C$ of the metric General Relativity is reduced
to its natural form. The natural form of canonical Hamiltonian provides
numerous advantages in actual applications to the metric GR, since the general
theory of dynamical systems with such Hamiltonians is well developed.
Furthermore, many analytical and numerically exact solutions for dynamical
systems with natural Hamiltonians have been found and described in detail. In
particular, based on this theory we can discuss an obvious analogy between
gravitational field(s) and few-particle systems where particles are connected
to each other by the Coulomb, or harmonic potentials. We also developed an
effective method which is used to determine various Poisson brackets between
analytical functions of the dynamical variables. Furthermore, such variables
can be chosen either from the straight, or dual sets of symplectic dynamical
variables which always arise in any Hamiltonian formulation developed for the
metric gravity.
  PACS number(s): 04.20.Fy and 11.10.Ef
