辛Runge-Kutta方法在卫星交会对接中的非线性动力学应用研究  

Nonlinear Dynamic Behavior of the Satellite Rendezvous and Docking Based on the Symplectic Runge-Kutta Method

作　　者：李庆军[1] 叶学华[1] 王博[1] 王艳[1] 

机构地区：[1]西北工业大学力学与土木建筑学院工程力学系,西安710072

出　　处：《应用数学和力学》2014年第12期1299-1307,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172239;11372252);高校博士点基金(20126102110023);中央高校基本科研业务费专项资金(310201401JCQ01001;3102014JCQ01041)~~

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.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.

关 键 词：卫星空间交会对接 非线性动力学 HAMILTON系统 辛Runge-Kutta方法 

分 类 号：O313.7[理学—一般力学与力学基础]