Using the transition to action variables of the newtonian problem in the numerical solution of the N-body problem

We propose an approach for overcoming the problem of close encounters in collisional systems, globular and open star clusters. As is well known, the numerical integration step in such systems, for example, during the formation of close binary stars, begins to fragment and the rate of calculations goes down to a complete stop. We show that using the perturbation theory in the proposed approach, one can isolate the singularity and to increase considerably the integration step without losing the physical effects that affect significantly the evolution of star clusters.