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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。
By unrolling the small thrust to a Fourier series with a near corner and by averaging the Gaussian perturbation equation over one orbital period, the thrust of the original equation is transformed into a control variable that is represented by only 14 Fourier coefficients. Simulation results show that the Gaussian equation after averaging reduces the computational cost significantly compared with Newton’s integral and has sufficient accuracy for small thrust. The reasons for the error when using the averaged Gauss equation to calculate the number of orbitals are studied. The influence of small thrust range and small thrust approximation on these errors is further analyzed. For the future non-Kepler orbits Kinetic analysis provides the theoretical basis and parameters.