The purpose of the present paper is a contribution to the study of steady-state probability density function (pdf) for mechanical systems of higher dimension, using Fokker-Planck (FKP) equation method. The article contains three parts. In parti I, we recall results about Ito stochastic differential equations and FKP equation and we set the problem. In part II, we present a result concerning the exact steady-sate pdf for a class of nonlinear dynamical systems in higher dimension. In part III, we develop a numerical method to solve the FKP equation in a reasonable higher dimension. We present a numerical example in a 12 dimension case.