Completely conservative, covariant numerical methodology

For a distance dependent potential ø, Newtonian dynamics is characterized by conservation of energy, linear momentum, and angular momentum. In addition, the basic dynamical equations are covariant, that is, invariant under fundamental coordinate transformations. In this paper, it is shown that related N-body problems can be solved numerically in such a fashion that, independently of the time step, the identical conservation laws continue to be valid for the approximating difference equations. In addition, the numerical method is covariant.