Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method
A satellite is considered to be moving relative to a nominal elliptical orbit, whose dynamics are usually described by the Tschaunner-Hempel equation (T-H equation). In this paper, we propose to transform the second-order time-varying system represented by the linear T-H equation with a second-order...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2023-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2023/1981979 |
| _version_ | 1827085619722977280 |
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| author | Sihui Liu Qingdao Huang |
| author_facet | Sihui Liu Qingdao Huang |
| author_sort | Sihui Liu |
| collection | DOAJ |
| description | A satellite is considered to be moving relative to a nominal elliptical orbit, whose dynamics are usually described by the Tschaunner-Hempel equation (T-H equation). In this paper, we propose to transform the second-order time-varying system represented by the linear T-H equation with a second-order matrix form into a first-order time-varying system. Then, the controllability of the first-order time-varying system is investigated with the matrix sequence method including e=0. Meanwhile, we study the observability of the first-order time-varying system with a specific form of measurement. The advantages of the matrix sequence method for controllability and observability analysis are tested by numerical examples, respectively. Dual theory is used to investigate the controllability and observability of the corresponding dual system of the T-H equation. The corresponding conclusions are obtained. |
| first_indexed | 2024-03-12T14:48:05Z |
| format | Article |
| id | doaj.art-aed98285127b45969736e8fe4a770298 |
| institution | Directory Open Access Journal |
| issn | 1687-5974 |
| language | English |
| last_indexed | 2025-03-20T04:23:49Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj.art-aed98285127b45969736e8fe4a7702982024-10-03T05:48:44ZengHindawi LimitedInternational Journal of Aerospace Engineering1687-59742023-01-01202310.1155/2023/1981979Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence MethodSihui Liu0Qingdao Huang1School of MathematicsSchool of MathematicsA satellite is considered to be moving relative to a nominal elliptical orbit, whose dynamics are usually described by the Tschaunner-Hempel equation (T-H equation). In this paper, we propose to transform the second-order time-varying system represented by the linear T-H equation with a second-order matrix form into a first-order time-varying system. Then, the controllability of the first-order time-varying system is investigated with the matrix sequence method including e=0. Meanwhile, we study the observability of the first-order time-varying system with a specific form of measurement. The advantages of the matrix sequence method for controllability and observability analysis are tested by numerical examples, respectively. Dual theory is used to investigate the controllability and observability of the corresponding dual system of the T-H equation. The corresponding conclusions are obtained.http://dx.doi.org/10.1155/2023/1981979 |
| spellingShingle | Sihui Liu Qingdao Huang Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method International Journal of Aerospace Engineering |
| title | Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method |
| title_full | Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method |
| title_fullStr | Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method |
| title_full_unstemmed | Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method |
| title_short | Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method |
| title_sort | controllability analysis of linear time varying t h equation with matrix sequence method |
| url | http://dx.doi.org/10.1155/2023/1981979 |
| work_keys_str_mv | AT sihuiliu controllabilityanalysisoflineartimevaryingthequationwithmatrixsequencemethod AT qingdaohuang controllabilityanalysisoflineartimevaryingthequationwithmatrixsequencemethod |