宇航学报

宇航学报 ›› 2011, Vol. 32 ›› Issue (10): 2103-2108.doi: 10.3873/j.issn.1000-1328.2011.10.002

• 飞行器设计与力学 • 上一篇    下一篇

自由段弹道扰动引力计算的球谐函数极点变换

郑伟, 谢愈, 汤国建   

  1. 国防科技大学航天与材料工程学院，长沙 410073
  • 收稿日期:2010-07-12 修回日期:2010-11-06 出版日期:2011-10-15 发布日期:2011-10-20
  • 作者简介:10001328（2011）10210306
  • 基金资助:
    收稿日期：20100712;
    \ 修回日期：20101106

Pole Transformation of Spherical Harmonic Method in Gravity Anomaly Calculation for Unpowered Phase Trajectory

ZHENG Wei, XIE Yu, TANG Guo   

  1. College of Aerospace and Materials Engineering，National University of Defense Technology，Changsha 410073，China
  • Received:2010-07-12 Revised:2010-11-06 Online:2011-10-15 Published:2011-10-20

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摘要： 为提高弹道导弹自由段扰动引力赋值速度，提出了自由段扰动引力计算的球谐函数极点变换一般方法。重点针对轨道动量矩与天球交点为极点及主动段关机点为极点两种情况，推导了考虑侧向偏差和地球旋转修正的扰动引力计算的球谐函数极点变换模型。仿真分析表明：从落点偏差来看，前者扰动引力计算相对误差为 1.89% ，后者为6.07%，满足诸元和制导精度要求。

关键词: 扰动引力, 球谐函数法, 极点变换, 弹道导弹

Abstract: To improve calculation efficiency of gravity anomaly for unpowered phase trajectory of ballistic missile, this paper proposed a general pole transformation method based on spherical harmonic method is proposed. Considering the lateral error and earth’s rotation correction, two kinds of pole transformation models are studied respectively. The pole of the first model is the intersection point between moment of momentum and celestial sphere, and the pole of the other model is the cutoff point of powered phase. The results show that the relative calculation error of the former pole transformation method is 1.89% and the latter is 6.07% from the point of view of impact point deviation, which can meet the accuracy requirement in firing data computation and guidance.

Key words: Gravity anomaly, Spherical harmonic method, Pole transformation, Ballistic missile

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