| 论完全泛函的变分问题 |
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| 引用本文： | 老大中.论完全泛函的变分问题[J].北京理工大学学报,2006,26(8):749-752. |
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| 作者姓名： | 老大中 |
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| 作者单位： | 北京理工大学,机电工程学院,北京,100081 |
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| 摘 要： | 研究变分法中依赖于任意个自变量、任意个多元函数和任意阶多元函数偏导数的完全泛函的变分问题;提出并证明了完全泛函的变分问题的定理,采用偏微分算子,给出了完全欧拉方程组. 该方程组涵盖了变分问题的各种欧拉方程. 通过两个算例验证了完全欧拉方程组的正确性.
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| 关 键 词： | 变分法 完全泛函 变分问题 偏微分算子 完全欧拉方程组 |
| 文章编号： | 1001-0645(2006)08-0749-04 |
| 收稿时间： | 1/6/2006 12:00:00 AM |
| 修稿时间： | 2006年1月6日 |
On the Variational Problems of the Complete Functional |
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| LAO Da-zhong.On the Variational Problems of the Complete Functional[J].Journal of Beijing Institute of Technology(Natural Science Edition),2006,26(8):749-752. |
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| Authors: | LAO Da-zhong |
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| Institution: | School of Mechatronic Engineering, Beijing Institute of Technology, Beiiing 100081, China |
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| Abstract: | The variational problems of the complete functional in calculus of variations are studied deperding on the arbitrary arguments,arbitrary multivariable functions and arbitrary-order partial derivatives of multivariable functions.The theorem of the variational problems of the complete functional is proposed and proved.The complete Euler equation set is obtained through the introduction of the partial differential operator.The complete Euler equation set contains all kinds of Euler equations of the variational problems.The correctness of the complete Euler equation set is verified with two functional examples. |
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| Keywords: | calculus of variations complete functional variational problems partial differential operator complete Euler equation set |
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