基于辛Runge-Kutta方法的太阳帆塔动力学特性研究

Dynamic behavior of sail tower SPS based on the symplectic Runge-Kutta method

空间太阳能发电作为获取清洁、可再生的能源的重要途径,受到了社会的广泛关注.本文基于Hamilton体系研究了太阳帆塔式空间太阳能电站在轨运行的动力学与系统的稳定问题.通过建立太阳帆塔简化结构模型和引入广义坐标以及广义动量,根据变分原理,得到Hamilton体系下太阳帆塔系统在轨运行的动力学控制方程;采用辛Runge-Kutta方法进行求解分析,并与传统的四阶Runge-Kutta方法对比,数值结果表明了辛Runge-Kutta方法能够保持系统的能量和系绳弹性振动的特性;最后,根据力学平衡原理得到了系统的平衡点,并通过数值算例研究了系统在平衡点附近的稳定性.

Space-based solar power as a promising approach to achieve clean and renewable energy had received extensive attention during the last several decades. The dynamics and stability of system of solar power satellite（SPS） in orbit were investigated through the application of Hamilton theory. First, the simplified structure model of sail tower SPS was built, and dynamic governing equation of simplified model of sail tower SPS in the Hamilton form were derived by introducing the concepts of generalized coordinates and generalized momentums and implementing variation method. Then, by numerically solving the equation through the application of the symplectic Runge-Kutta method and comparing the results with the traditional Runge-Kutta method, numerical examples demonstrated that the results achieved by the symplectic Runge-Kutta method indicated the energy preservation as well as the vibrational amplitude of the tether. Finally, the equilibrium points was calculated based on mechanical balance principle. Besides, the stability of the considered system at the equilibrium points was analyzed via numerical examples.