| 一阶系统自伴随条件和Lagrange函数的构造 |
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| 引用本文： | 丁光涛.一阶系统自伴随条件和Lagrange函数的构造[J].动力学与控制学报,2012,10(1):1-4. |
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| 作者姓名： | 丁光涛 |
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| 作者单位： | 安徽师范大学物理与电子信息学院,芜湖 241000 |
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| 摘 要： | 重新研究一阶系统变分法逆问题,修正了某些文献关于一阶微分方程组自伴随条件的失误,导出了把一阶系统化为自伴随形式的变换矩阵所满足的方程,列出了构造自伴随一阶系统Lagrange函数的两种方法.举例说明所得结果的应用.
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| 关 键 词： | 一阶微分方程系统 逆问题 自伴随条件 一阶Lagrange函数 |
| 收稿时间： | 2011/6/11 0:00:00 |
| 修稿时间： | 2011/6/27 0:00:00 |
The conditions of self-adjointness and the constraction of Lagrangian for a first-order system |
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| Ding Guangtao.The conditions of self-adjointness and the constraction of Lagrangian for a first-order system[J].Journal of Dynamics and Control,2012,10(1):1-4. |
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| Authors: | Ding Guangtao |
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| Affiliation: | Ding Guangtao (College of Physics and Electronic Information,Anhui Normal University,Wuhu 241000,China) |
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| Abstract: | The inverse problem of the calculus of variations for the first-order system was restudied. The errors on the conditions of self-adjointness for a system of the first-order ordinary differential equations in some literatures were amend. The equations to determine the matrices of the self-adoint transformations for the first-order system were obtained. Two methods of constraction of the Lagrangians for the first-order self-adjoint system were presented. An example was given to illustrate the application of the result. |
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| Keywords: | system of first-order ordinary differential equations inverse problem conditions of self-adjointness first-order Lagrangian |
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