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

doi:10.11947/j.AGCS.2018.20170082

Acta Geodaetica et Cartographica Sinica ›› 2018, Vol. 47 ›› Issue (4): 455-464.doi: 10.11947/j.AGCS.2018.20170082

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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)

Abstract

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

CLC Number:

P228

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

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