基于高阶兰伯特算法的碎片云密度演化分析

Debris cloud evolution analysis method based on higher-order Lambert problems

空间目标解体形成的碎片云在太空不断演化,持续威胁着在轨航天器的安全运行.传统方法多将碎片云视为独立个体的集合,对个体进行推演以获取整体演化特性.这类方法虽易于实现,但需要大量样本以致效率较低.考虑到碎片分布的不确定性特征,可利用概率密度变换方法来计算碎片云在空间的密度分布.基于微分代数技术构建了高阶兰伯特算法,再求解系统雅可比的高阶近似,获得了碎片云密度的高阶展开式.通过对解体碎片云的密度演化分析计算表明,采用高阶方法可将计算效率提高10倍,得到的结果相对误差在1%以内.

The debris cloud formed from the fragmentation of space objects evolves under orbital dynamics,pose a continuous threat to the safe of spacecraft.Traditionally,the debris cloud is regarded as a collection of independent fragments,and these fragments are propagated to obtain the overall evolution characteristics.This method requires a large number of samples and is therefore inefficient.In view of the uncertainty of the debris distribution,the density of the debris cloud can be directly calculated based on the boundary value problem and the probability density transformation.The high-order Lambert solution is constructed based on differential algebra,and the high-order Jacobian of the system is computed,which is used in the transformation of fragment distribution probability.The numerical examples show that the high-order methods can increase the calculation efficiency by 10 times,and the relative error of the results is within 1%.