中文摘要：

引入差分离散变分原理,得到了Hamilton形式下的Kepler系统的差分方程、能量演化方程和系统的保辛数值算法格式,给出了离散Kepler系统的Noether定理.数值计算Kepler系统的运动轨迹、时间历程和守恒量,并和传统的4阶R-K方法比较,说明离散变分算法能够较好地保持系统的稳定性和具有较高的计算精度.

英文摘要：

The canonical Hamiltonian difference equations and the energy equation of the Kepler system were proposed by introducing the discrete difference variational principle. The symplectic numerical algo- rithm was proposed for this equation. The discrete Noether theorem of the Kepler system was presented by means of difference discrete variational principle with the difference being regarded as an entire geometric object. The numerical calculations of the trajectory, the sollution and the three types of conserved quanti- ties were shown. The difference discrete variational method preserved the exactness and the invariant quantity.