Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series
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,...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2016/9747289 |
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| author | Ying-Jing Qian Xiao-Dong Yang Lei-Yu Yang Wei Zhang |
| author_facet | Ying-Jing Qian Xiao-Dong Yang Lei-Yu Yang Wei Zhang |
| author_sort | Ying-Jing Qian |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6ae3ddab4abf42b1a7f80fd980b9f62f |
| institution | Kabale University |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-6ae3ddab4abf42b1a7f80fd980b9f62f2025-08-20T03:34:00ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742016-01-01201610.1155/2016/97472899747289Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial SeriesYing-Jing Qian0Xiao-Dong Yang1Lei-Yu Yang2Wei Zhang3Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, ChinaBeijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, ChinaThe 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.http://dx.doi.org/10.1155/2016/9747289 |
| spellingShingle | Ying-Jing Qian Xiao-Dong Yang Lei-Yu Yang Wei Zhang Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series International Journal of Aerospace Engineering |
| title | Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series |
| title_full | Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series |
| title_fullStr | Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series |
| title_full_unstemmed | Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series |
| title_short | Approximate Analytical Methodology for the Restricted Three-Body and Four-Body Models Based on Polynomial Series |
| title_sort | approximate analytical methodology for the restricted three body and four body models based on polynomial series |
| url | http://dx.doi.org/10.1155/2016/9747289 |
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