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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。
At the same time, the tethered satellite system dynamics simulation considering the tether quality, elasticity, deformation and other factors is a complex problem of solving nonlinear partial differential equations. In order to construct continuous mode function, the dynamic model of tethered satellite system based on Newton’s theorem and generalized Hooke’s law is adopted. Based on the Ritz method, the displacement function is constructed as a linear combination of the modal function and the coefficient to be solved, and then the originally complex nonlinear partial differential equation is transformed into the more common nonlinear ordinary differential equation. The simulation example is based on the fact that the rope system is freely deployed at 5 ° from the stable equilibrium position and the out-of-plane angle. The numerical simulation proves the basic dynamic characteristics of the rope system. At the same time, we find that the tether is weakly bent during free expansion and oscillation Not efficient enough.