Discrete variational principle and the first integrals of the conservative holonomic systems in event space

The intent of this paper is to show that first integrals of discrete equation of motion for the conservative holonomic systems can be determined explicitly by investigating the invariance properties of the discrete Lagrangian in event space. The result obtained is a discrete analogue of Noether’s theorem in the calculus variations. The two examples are given to illustrate the applications of the result.