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中文摘要：
卫星交会对接问题是实现太空平台等空间系统的关键问题之一.考虑了由于地球引力作用而引起的卫星交会对接中的非线性动力学问题.首先,采用能量方法给出Lagrange函数;然后,通过引入广义坐标和广义动量,以及Legendre变换,得到Hamilton方程;随后,采用辛Runge-Kutta方法求解该Hamilton方程,并与传统的四阶Runge-Kutta方法对比.数值结果表明：辛Runge-Kutta方法能够在积分过程中长时间保持系统的固有特性,为天体动力学问题的研究提供了良好的数值方法.
英文摘要：
The simulation of the satellite rendezvous and docking is one of most important problems for space platforms and so on. The nonlinear dynamic behavior of the satellite rendez- vous and docking was investigated. According to the energy principle, the Lagrange function was given; then, the generalized coordinates, generalized momentum and Legendre transforma- tion were introduced to derive the Hamilton equations; both the symplectic Runge-Kutta method and the 4th-order Runge-Kutta method were comparatively used to solve the Hamilton equa- tions. Through numerical analysis, it is easily found that the natural properties of the nonlinear dynamic system are well preserved with the symplectic Runge-Kutta method, especially in the long-time chasing cases. The proposed symplectic method is applicable to the related astrody- namic problems.
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