基于傅立叶平均法下的连续小推力动力学分析

通过将小推力展开为偏近点角的傅立叶级数,并对高斯摄动方程在一个轨道周期上的平均,将原方程的推力转化为仅由14个傅立叶系数表示的控制变量。仿真计算表明,平均化后的高斯方程使计算量与牛顿积分相比显著减少,且对小推力而言有足够的精度。对利用平均化后的高斯方程计算轨道根数时产生误差的原因进行了研究,并进一步分析小推力的范围和小推力近似表达式对上述误差的影响,为今后小推力下非开普勒轨道动力学分析提供了理论依据和参数。

Dynamic analysis of continuous low-thrust based on fourier average method

Each component of the thrust vector was expanded as Fourier series in eccentric anomaly and Gauss variational equations were averaged over one orbit period,then the thrust vector was translated to a variable controlled by fourteen Fourier’s parameters.Simulation results show that these secular equations are sufficient to accurately determine a low-thrust spiral trajectory with significantly reduced computation as compared with integration of the full Newtonian problem.In addition,error causes of orbit elements witch were calculated by the averaged Gauss equations were studied,and influence of low-thrust range and approximate expressions on the error was further analyzed,providing theoretical basis and parameters for dynamic analysis of the Non-Keplerian orbits of low-thrust.