| 关于Birkhoff表示的Lagrange像的研究 |
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| 引用本文： | 丁光涛. 关于Birkhoff表示的Lagrange像的研究[J]. 物理学报, 2010, 59(1): 15-19 |
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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： | 研究运动微分方程Birkhoff表示的Lagrange像.得出二阶Lagrange函数应满足的条件,在此条件下广义Lagrange方程为二阶微分方程组;提出新的求解Lagrange力学逆问题路线;指出在此问题研究中曾发生过的失误.举例说明所得结果的应用.
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| 关 键 词： | Birkhoff表示 Lagrange像 逆问题 二阶Lagrange函数 |
| 收稿时间： | 2009-03-14 |
A study on the Lagrangian image of the Birkhoffian representations |
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| Ding Guang-Tao. A study on the Lagrangian image of the Birkhoffian representations[J]. Acta Physica Sinica, 2010, 59(1): 15-19 |
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| Authors: | Ding Guang-Tao |
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| Abstract: | The Lagrangian image of the Birkhoffian representations is studied. The conditions that the second-order Lagrangians should satisfy are obtained, under which the generalized Lagrange equations are second-order differential equations. A new way for solving the inverse problem in Lagrange mechanics is presented. An error made in the study by some author is pointed out. Two examples are given to illustrate the application of the result. |
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| Keywords: | Birkhoffian representations Lagrangian image inverse problem second-order Lagrangian |
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