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针对限制性三体问题中的平动点双脉冲转移,提出一种高效的计算方法。通过利用基于二维插值的数值流形近似方法对流形进行近似计算,同时利用二体模型下的圆锥曲线近似流形拼接段,根据经典轨道要素推导得到完成拼接所需的速度增量,避免在优化过程中对流形的重复积分计算,以及在三体模型下对拼接段的迭代计算,从而显著提高计算效率。然后推导得到三体问题下的主矢量理论,可将其用于对优化所得的双脉冲转移轨道进行燃料最优性的验证。最后,以航天器从近地圆轨道到地月系L1点的halo轨道的双脉冲转移为例进行数值仿真,验证数值流形近似算法和二体模型近似脉冲的有效性,并表明该方法在优化过程中具有高效性。
Aiming at the double pulse transfer of the translational point in the restricted three-body problem, an efficient calculation method is proposed. By using the numerical manifold approximation method based on two-dimensional interpolation to approximate the manifold, and using the conic curve in the two-body model to approximate the manifold splicing segment, the incremental velocity needed to complete the splicing is deduced according to the classical orbital elements, In the process of optimization, iterative integral calculation of manifolds and iterative calculation of splicing sections under three-body model are carried out, so as to improve computational efficiency significantly. Then, the principal vector theory under the three-body problem is deduced, which can be used to verify the fuel optimality of the optimized two-pulse transfer orbit. Finally, the numerical simulation of the double-pulse transfer from spacecraft near-Earth orbit to the halo orbit at L1 point of the earth-moon system is performed to verify the numerical manifold approximation algorithm and the approximation of the two-body model. Optimize the process with high efficiency.