中国空间科学技术

中国空间科学技术 ›› 2011, Vol. 31 ›› Issue (6): 73-80.doi: 10.3780/j.issn.1000-758X.2011.06.011

• 技术交流 • 上一篇    

基于里兹法的绳系卫星动力学仿真

冯杰, 鲜勇, 雷刚   

  1. （第二炮兵工程学院，西安 710025）
  • 收稿日期:2011-04-06 修回日期:2011-12-25 出版日期:2011-12-25 发布日期:2011-12-25
  • 作者简介:冯杰 1982年生，2008年获第二炮兵工程学院飞行器设计专业硕士学位，现于第二炮兵工程学院攻读飞行器设计专业博士学位。研究方向为绳系卫星动力学与控制。
  • 基金资助:

    国家863计划资助项目

Dynamical Simulation of Tethered Subsatellite Based on Ritz′s Method

 FENG  Jie, XIAN  Yong, LEI  Gang   

  1. （The Second Artillery Engineering College, Xi′an 710025）
  • Received:2011-04-06 Revised:2011-12-25 Published:2011-12-25 Online:2011-12-25

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摘要： 同时考虑系绳质量、弹性、形变等因素的绳系卫星系统动力学仿真是复杂的非线性偏微分方程求解问题。为便于构造连续型模态函数，采用了基于牛顿定理及广义胡克定律建立的绳系卫星系统动力学模型。基于里兹法将位移函数构造为模态函数与待求系数的线性组合，进而将原本复杂的非线性偏微分方程转化为较常见的非线性常微分方程。仿真算例基于绳系系统从稳定平衡位置及面外角5°自由展开来进行，数值仿真印证了绳系系统的基本动力学特性，同时发现系绳自由展开及摆动过程中有微弱弯曲现象且计算效率不够高。

关键词: 动力学仿真, 里兹法, 自由展开, 绳系卫星

Abstract: Considering the tether′s mass, elasticity and deformation，the emphasis of the dynamical simulation problem for a tethered subsatellite is to solve the non-linear partial  differential equations.To establish the continuous mode functions, the dynamical models were built by Mankala method based on Newton's theorem and generalized Hook′s laws. The continuity of the numerical results was achieved via linear compounding of mode technique with polynomial shape functions by Ritz′s method. Hence, the complicated partial differential equations were transformed to ordinary differential equations. Based on the sub-satellite′s free deployment from the steady balance position and 5 degrees out of the plane, the numerical simulations were conducted. The simulation results show slight bending and other basic dynamical characteristics during tether′s swing and free deployment. Meanwhile, the calculation efficiency of Ritz′s method is low.

Key words: Dynamical simulation, Ritz′s method, Free deployment, Tethered subsatellite