拉格朗日/高斯无奇点卫星运动方程推导与分析

doi:10.11947/j.AGCS.2018.20170082

测绘学报 ›› 2018, Vol. 47 ›› Issue (4): 455-464.doi: 10.11947/j.AGCS.2018.20170082

拉格朗日/高斯无奇点卫星运动方程推导与分析

蒋春华^1,2, 徐天河¹, 乔晶⁴, 杜玉军¹, 王庆³, 许国昌¹

1. 山东大学空间科学研究院, 山东威海 264209;
2. 西安测绘研究所地理信息工程国家重点实验室, 陕西西安 710054;
3. 东南大学仪器科学与工程学院, 江苏南京 210096;
4. 香港理工大学, 香港 999077

收稿日期:2017-02-23 修回日期:2017-07-19 出版日期:2018-04-20 发布日期:2018-05-02
通讯作者: 许国昌 E-mail:gcxu@sdu.edu.cn
作者简介:蒋春华(1988-),女,博士生,研究方向为轨道理论与GNSS高精度数据处理的理论与方法。E-mail:jiangchunhua@sdu.edu.cn
基金资助:
国家自然科学基金（41574025）；地理信息工程国家重点实验室开放基金（SKLGIE2016-M-2-1）；国家重点研发计划（2016YFB0501900）

Derivation and Analysis of Singular-free Lagrangian/Gaussian Equations of Planetary Motion

JIANG Chunhua^1,2, XU Tianhe¹, QIAO Jing⁴, DU Yujun¹, WANG Qing³, XU Guochang¹

1. Institute of Space Sciences, Shandong University, Weihai 264209, China;
2. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China;
3. Master of Instrument and Meter Engineering, Southeast University, Nanjing 210096, China;
4. Hong Kong Polytechnic University, Hongkong 999077, China

Received:2017-02-23 Revised:2017-07-19 Online:2018-04-20 Published:2018-05-02
Supported by:
The National Natural Science Foundation of China(No. 41574025);The Open Fund of the State Key Laboratory of Geo-information Engineering(No. SKLGIE2016-M-2-1);The National Key Research and Development Program of China(No. 2016YFB0501900)

摘要/Abstract

摘要： 针对卫星轨道理论中的奇点问题，对拉格朗日/高斯无奇点卫星运动方程做了深入的分析和探索，从原始拉格朗日和高斯运动方程及其物理意义出发，考虑圆轨道、圆赤道轨道和赤道轨道3种奇点情况，推导了一种新的拉格朗日/高斯无奇点卫星运动方程，并探讨了方程的连续性。该方程消除了零因子，解决了卫星运动方程的奇点问题。

关键词: 拉格朗日/高斯无奇点运动方程, 奇点问题, 卫星轨道, 连续性

Abstract: Aiming at the singularity problem in satellite orbit theory,the singularity-free Lagrangian/Gaussian equations of motion is analyzed.Considering the original and physical meaning of the Lagrangian and Gaussian equations of motion,a new Lagrangian/Gaussian singularity-free disturbed equations of motion is proposed and then discussed in three cases:the circular orbit,equatorial orbit,circular and equatorial orbit.Besides,the continuity of these equations is explored.The proposed equations eliminate the zero factor and in this way the singularity problem in the orbital mechanics is solved.

Key words: singularity-free Lagrangian/Gaussian equations of motion, singularity problem, satellite orbit, continuity

中图分类号:

P228

蒋春华, 徐天河, 乔晶, 杜玉军, 王庆, 许国昌. 拉格朗日/高斯无奇点卫星运动方程推导与分析[J]. 测绘学报, 2018, 47(4): 455-464.

JIANG Chunhua, XU Tianhe, QIAO Jing, DU Yujun, WANG Qing, XU Guochang. Derivation and Analysis of Singular-free Lagrangian/Gaussian Equations of Planetary Motion[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(4): 455-464.

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拉格朗日/高斯无奇点卫星运动方程推导与分析

Derivation and Analysis of Singular-free Lagrangian/Gaussian Equations of Planetary Motion

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