  Because of absence of time derivatives from scalar potential as a generalized
coordinate of gravitation field (GF) in action of nonrelativistic gravitating
system, application of the Hamilton method for description of GF mechanics was
impossible. In the paper a transformation of the generalized coordinate of GF,
that is based on continuity equation and minimal action principle, is proposed.
A potential vector is introduced that is similar to fixing of Hamilton gauge of
the electromagnetic field. This transformation gives possibility of the
calculation a Hamilton function, removes mathematical troubles of the Jeans
theory (Jeans swindle) and allows to construct kinetic theory of GF using
statistical mechanics methods.
