In the article a mapping approach based on nonlinear matrix integration for longterm spin-orbit dynamics simulation is briefly described. Using this technique the nonlinear effects of spin dynamics in an electrostatics storage ring are investigated. Namely, the fringe fields, the energy conservation law and the random field errors are considered. The necessity of examination of such effects arises, for example, in the storage ring design for search the Electrical Dipole Moment of proton and deuteron. The EDM ring is proposed to measure EDM using the spin transformation of polarized particle in the magneto-electrostatic elements of the ring. The article consists of short description of the spin-orbit simulation results based on the nonlinear model.