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| Solving time-varying periodic coefficient Riccati differential equations via Fourier series and precise integration method |
| Received:December 07, 2007 |
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| DOI：10.7511/jslx20096003 |
| KeyWord:linear time-varying system periodic Riccati differential equations Fourier series precise integration method |
| Author | Institution |
| 彭海军 |
大连理工大学 运载工程与力学学部工程力学系 工业装备结构分析国家重点实验室,大连 |
| 吴志刚 |
大连理工大学 运载工程与力学学部工程力学系 工业装备结构分析国家重点实验室,大连 |
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| Abstract: |
| With Fourier series expansions, an efficient numerical algorithm is proposed for solving time-varying periodic coefficient Riccati differential equations. Firstly, periodic coefficients are expanded in terms of Fourier series, and the state transformation matrix of the associated Hamiltonian system is evaluated by the precise integration method. Then, by employing the Riccati transformation method, recursive formulae for time-varying periodic coefficient Riccati differential equations are derived, which consist of blocks of the state transformation matrix. At last, the efficiency and reliability of the periodic character based numerical method is demonstrated by two examples. |
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