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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。
The nonlinear internal resonance problem of tethered satellite system due to the coupling of tether and pitching motions was studied. Firstly, the nonlinear dynamic model of the elliptical orbit elliptical orbiting elastic tethered satellite system during state keeping is established by Kane equation, and the possible internal resonance conditions are analyzed. Then, based on the multi-scale method, the analytic solution of the internal resonance resonance equation and its Jacobi elliptic function representation is obtained. The results show that the orbital perturbation does not affect the internal resonance, the internal resonance coupling vibration caused by the system parameters will be transmitted between the two modes, and the modulation period depends on the initial modal amplitude. At certain tuning parameters, the modal amplitude appears saturated.