| 引用本文: | 常晓华.考虑地球非球形引力摄动影响的自由段弹道解析解.[J].国防科技大学学报,2018,40(4):80-86.[点击复制] |
| CHANG Xiaohua.Analytical solution for free flight trajectory considering earth non spherical gravitation perturbation[J].Journal of National University of Defense Technology,2018,40(4):80-86[点击复制] |
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| 考虑地球非球形引力摄动影响的自由段弹道解析解 |
| 常晓华 |
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(北京宇航系统工程研究所， 北京 100076)
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| 摘要: |
| 针对地球非球形引力摄动影响下的自由段弹道快速计算问题，在非正交坐标系内建立考虑J2项摄动的地球引力作用下的运动微分方程，在轨道坐标系内建立扰动引力作用下的运动微分方程，并计算天向扰动引力加速度对应的质量偏差，进而通过椭圆轨道以修正J2项摄动运动微分方程；在建立上述运动微分方程解析解的基础上，给出了地心坐标系内弹道飞行器位置和绝对速度的表达式，从而提出了J2项摄动引力和扰动引力作用下的自由段弹道解析计算方法。仿真分析表明：该方法具有较高的计算效率，落点位置偏差小于20 m，满足弹道飞行器高精度实时制导、轨迹预测等应用需求。 |
| 关键词: J2项摄动 扰动引力 解析解 弹道飞行器 |
| DOI：10.11887/j.cn.201804013 |
| 投稿日期：2017-05-13 |
| 基金项目:国家部委基金资助项目（613222） |
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| Analytical solution for free flight trajectory considering earth non spherical gravitation perturbation |
| CHANG Xiaohua |
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(Beijing Institute of Astronautical System Engineering, Beijing 100076, China)
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| Abstract: |
| In order to solve the fast calculation of the free trajectory considering the effects of the earth non-spherical gravitation, the differential equations of motion under the earth gravitation including the J2-perturbation were established in the non-orthogonal coordinate system, and the differential equations of motion under disturbing gravity were established in the orbital coordinate system. The acceleration of upward disturbing gravity was equivalent to the mass deviation of the earth, and introduced into the standard elliptical orbit. The differential equations under J2-perturbation were modified, and the parameters of the position and velocity were calculated under the analytical solution. The simulation results show that the analytic solution has a higher efficiency, and the position error of impact point is within 20 meters. The analytic solution satisfies the requirement of the real-time guidance and orbit forecast. |
| Keywords: J2-perturbation disturbing gravity analytical solution ballistic vehicle |
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