辛Runge-Kutta方法在卫星交会对接中的非线性动力学应用研究

李庆军; 叶学华; 王博; 王艳

doi:10.3879/j.issn.1000-0887.2014.12.002

辛Runge-Kutta方法在卫星交会对接中的非线性动力学应用研究

doi: 10.3879/j.issn.1000-0887.2014.12.002

西北工业大学力学与土木建筑学院工程力学系, 西安 710072

基金项目: 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）

详细信息

作者简介:
李庆军（1992—），男，广东人，博士生(通讯作者. E-mail: lqingjun@163.com).

中图分类号: O313.7
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- 被引次数: 0
出版历程
- 收稿日期: 2014-06-03
- 修回日期: 2014-10-09
- 刊出日期: 2014-12-15

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

Department of Engineering Mechanics, School of Mechanics and Civil.& Architecture,Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds: The National Natural Science Foundation of China（11172239;11372252）

摘要

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.
- 卫星空间交会对接 /
- 非线性动力学 /
- Hamilton系统 /
- 辛Runge-Kutta方法
Abstract: 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 rendezvous and docking was investigated. According to the energy principle, the Lagrange function was given; then, the generalized coordinates, generalized momentum and Legendre transformation 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 equations. 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 astrodynamic problems.
- satellite rendezvous and docking /
- nonlinear dynamics /
- Hamilton system /
- symplectic RungeKutta method

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参考文献(18)

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