Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series
Joint Authors
Zhang, Wei
Yang, Xiao-Dong
Qian, Ying-Jing
Yang, Lei-Yu
Source
International Journal of Aerospace Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-10-19
Country of Publication
Egypt
No. of Pages
8
Abstract EN
The restricted three-body problem (R3BP) and restricted four-body problem (R4BP) are modeled based on the rotating frame.
The conservative autonomous system for the R3BP and nonautonomous system with period parametric resonance due to the fourth body are derived.
From the vibrational point of view, the methodology of polynomial series is proposed to solve for these problems analytically.
By introducing the polynomial series relations among the three directions of motion, the three-degree-of-freedom coupled equations are transferred into one degree-of-freedom containing the full dynamics of the original autonomous system for the R3BP.
As for the R4BP case, the methodology of polynomial series combined with the iterative approach is proposed.
During the iterative approach, the nonautonomous system can be treated as pseudoautonomous equation and the final polynomial series relations and one-degree-of-freedom system can be derived iteratively.
American Psychological Association (APA)
Qian, Ying-Jing& Yang, Xiao-Dong& Yang, Lei-Yu& Zhang, Wei. 2016. Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series. International Journal of Aerospace Engineering،Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1105060
Modern Language Association (MLA)
Qian, Ying-Jing…[et al.]. Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series. International Journal of Aerospace Engineering No. 2016 (2016), pp.1-8.
https://search.emarefa.net/detail/BIM-1105060
American Medical Association (AMA)
Qian, Ying-Jing& Yang, Xiao-Dong& Yang, Lei-Yu& Zhang, Wei. Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series. International Journal of Aerospace Engineering. 2016. Vol. 2016, no. 2016, pp.1-8.
https://search.emarefa.net/detail/BIM-1105060
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1105060