关键词: 重力场, 运动积分, Runge-Lenz矢量, 哈密顿-雅可比方程, 简并性, 分离变量, 可积性

Abstract: The integrals of the motion of particle system in gravity field are discussed,the relation between Runge-Lenz type vector and constants in the separation variable method is analyzed.The integrability of system and its relation with the integrals of motion are also studied.

Key words: gravity field, motion integral, Runge-Lenz vector, Hamilton-Jacobi equation, degeneracy, separation variable, integrability