面内弹性绳系卫星系统的内共振
夏洁，庞兆君，金栋平
摘要:研究了绳系卫星系统因系绳弹性和俯仰运动相耦合而引起的非线性内共振问题。首先应用Kane方程建立了面内椭圆轨道两体弹性绳系卫星系统在状态保持阶段的非线性动力学模型,分析了可能发生的内共振条件。然后,基于多尺度方法获得内共振下的调制方程及其Jacobi椭圆函数表示的解析解。结果表明,轨道摄动因素不会影响内共振,系统参数引起的内共振耦合振动会在两个模态之间相互传递,其调制周期取决于初始模态幅值。在一定的调谐参数上,模态振幅出现饱和现象。
关键词：绳系卫星；椭圆函数；内共振；饱和
Inner resonance of an in-plane elastic tethered satellite system
Jie Xia, Zhaojun Pang, Dongping Jin
Abstract：This paper is devoted to the nonlinear inner resonance of an in-plane tethered satellite system coupled by the elasticity of the tether and pitching motion.A planar nonlinear dynamical model of the tethered satellite system that moves in an elliptical orbit during state-keeping stage is established using Kane’s equation method and the condition of inner resonance is analyzed.And then,the modulation equations are obtained based on the method of multiple scales,and the analytical solutions in terms of Jacobi elliptic function are given as well.Subsequently,the parameter conditions for periodic and non-periodic oscillations are analyzed using graphical solution method.The results show that orbital eccentricity does not affect the resonance.Under resonant responses,the system energy would have an exchange between the two modes of oscillation;the period of modulation would vary with the initial values of mode amplitudes.It is found that there exist the saturation phenomena for mode amplitude once the tuning parameters fall within a small region.
Keyword：tethered satellite system; elliptic function; resonance; saturation
原文链接：http://www.cnki.com.cn/Article/CJFDTotal-ZDGC201203003.htm
