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Reduction of the canonical Hamiltonian of the metric GR to its natural form

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