Abstract
The computer simulation from the first principles allows us to obtain results for systems consisting ofmany particles and interacting according to the Coulomb law (plasma, star clusters and astrophysicalobjects). In this work, the methodology of simulation for Coulomb systems is investigated. The influenceof rounding errors, integration errors of reversible Newton equations is studied on the characteristics ofCoulomb collisions on the basis of the consideration of several model problems. The trajectories of twoparticles attracted to the positively charged force center are got for various initial coordinates andvelocities and also their energetic natures are researched. It is shown that the symmetries are broken andthe particle paths are destroyed due to rounding errors and calculation errors. The degree of deviationfrom symmetry is described by the value of the Lyapunov exponent, which characterizes the chaos andturbulence in plasmas for the system. The results can be also extended to the system of gravitatingmasses.