  A new method is presented to describe the evolution of the orbital-parameter
distributions for an initially universal binary population in star clusters by
means of the currently largest existing library of N-body models. It is
demonstrated that a stellar-dynamical operator exists, which uniquely
transforms an initial orbital parameter distribution function for binaries into
a new distribution depending on the initial cluster mass and half-mass radius,
after some time of dynamical evolution. For the initial distribution the
distribution functions derived by Kroupa (1995a,b) are used, which are
consistent with constraints for pre-main sequence and Class I binary
populations. Binaries with a lower energy and a higher reduced-mass are
dissolved preferentially. The stellar-dynamical operator can be used to
efficiently calculate and predict binary properties in clusters and whole
galaxies without the need for further N-body computations. For the present set
of N-body models it is found that the binary populations change their
properties on a crossing time-scale such that the stellar dynamical operator
can be well parametrized as a function of the initial cluster density.
Furthermore it is shown that the binary-fraction in clusters with similar
initial velocity dispersions follows the same evolutionary tracks as a function
of the passed number of relaxation-times. Present-day observed binary
populations in star clusters put constraints on their initial stellar densities
which are found to be in the range 10^2 - 2x10^5 M_sun pc^-3 for open clusters
and a few x 10^3 - 10^8 M_sun pc^-3 for globular clusters, respectively.
