  The exact equations of motion for microscopic density of classical particles
number with account of inter-particle interactions and external field in closed
form are derived. An integral equation for equilibrium distributions of the
particles is deduced. No statistical or probabilistic hypotheses and assumption
in these deductions have been used. Some well known results of equilibrium
statistical mechanics are deduced from the obtained equations as simple
limiting cases. The wave equation for almost homogeneous systems with
inter-particle interactions are obtained. Connection between inter-particle
potential and dispersion law of sound is established.
  Keywords: Many-body systems dynamics; inter-atomic potentials; phase
equilibrium
  PACS 05.20.-y; 05.10.-a; 05.70.Ln
