Consider a system of N classical particles. The particles a confined to
a particular region of space by a ``container'' of volume V.
The particles have a finite kinetic energy and are therefore in constant
motion, driven by the forces they exert on each other (and any external
forces which may be present). At a given
instant in time t, the Cartesian positions of the particles are
. The time evolution of the positions of the
particles is then given by Newton's second law of motion:
where 
are the forces on each of the N particles
due to all the other particles in the system. The notation 
.
N
Newton's equations of motion constitute a set of 3N coupled second order
differential equations. In order to solve these, it is necessary to specify
a set of appropriate initial conditions on the coordinates and their
first time derivaties, 
.
Then, the solution of Newton's equations gives the complete set of
coordinates and velocities for all time t.