IRREVERSIBILITY IN CLASSICAL MECHANICS AS A CONSEQUENCE OF POINCARE-GROUP

In the post-Galilean approximation of Poincare Group (i.e. in the appr oximation in which the corrections of order O(c(-2)), c denoting the l ight velocity, to the Galilei group are taken in account) the Lagrangi ans are singular on a submanifold of the phase space. It is a local si ngularity, which differs from the ones considered by Dirac. The dynami cal properties are essentially peculiar on the studied singular surfac es.(1-4) In particular, on some submanifolds of the singular manifold the velocities are not determined uniquely: in each point of the subma nifold we get the infinite set of components of velocity. It means the loss of the reversibility of the motion in a sense that transformatio n of the phase space, corresponding to Lagrangian, has not a property of a group. It is shown, that if the values of the derivates of the mo lecular potentials are large enough the irreversibility of motion take s place. As consequence we obtain the relaxation to the equilibrium. T his property does not exist if the Lagrangian is invariant with respec t to Galilei Group.