ファイル | |
言語 |
英語
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著者 |
Ishibashi, Kazuki
Department of Electronic Control Engineering, National institute of Technology, Hiroshima College,
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内容記述(抄録等) | As is well known, Mathieu’s equation is a representative of mathematical models describing
parametric excitation phenomena. This paper deals with the oscillation problem for Mathieu’s equation with two frequencies. The ratio of these two frequencies is not necessarily a rational number. When the ratio is an irrational number, the coefficient of Mathieu’s equation is is quasi-periodic, but not periodic. For this reason, the basic knowledge for linear periodic systems such as Floquet theory is not useful. Whether all solutions of Mathieu’s equation oscillate or not is determined by parameters and frequencies. Our results provide parametric conditions to guarantee that all solutions are nonoscillatory. The advantage of the obtained parametric conditions is that it can be easily checked. Parametric nonoscillation region is drawn to understand these results easily. Finally, several simulations are carried out to clarify the remaining problems. |
主題 | Nonoscillation
Parametric excitation
Mathieu’s equation
Frequencies
Quasi-periodic
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掲載誌名 |
Applied Mathematics and Computation
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巻 | 346
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開始ページ | 491
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終了ページ | 499
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ISSN | 0096-3003
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発行日 | 2019-04
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DOI | |
出版者 | Elsevier
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資料タイプ |
学術雑誌論文
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ファイル形式 |
PDF
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著者版/出版社版 |
著者版
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部局 |
総合理工学部
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