| 一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法 |
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| 引用本文： | 丁光涛.一维变系数耗散系统Lagrange函数和Hamilton函数的新构造方法[J].物理学报,2011,60(4):44503-044503. |
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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： | 提出构造二阶微分方程的Lagrange函数和Hamilton函数的新路径. 将二阶方程写成一阶方程组并构造出对应的一阶Lagrange函数后,直接从一阶Lagrange函数导出二阶Lagrange函数和Hamilton函数. 利用上述方法得到若干耗散和类耗散系统的一阶和二阶Lagrange函数以及Hamilton函数;讨论了这种方法的优点. 举例说明所得结果的应用.
关键词：
逆问题
耗散系统
Lagrange函数
Hamilton函数
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| 关 键 词： | 逆问题 耗散系统 Lagrange函数 Hamilton函数 |
| 收稿时间： | 2010-06-10 |
| 修稿时间： | 7/5/2010 12:00:00 AM |
A new approach to the construction of Lagrangians and Hamiltonians for one-dimensional dissipative systems with variable coefficients |
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| Ding Guang-Tao.A new approach to the construction of Lagrangians and Hamiltonians for one-dimensional dissipative systems with variable coefficients[J].Acta Physica Sinica,2011,60(4):44503-044503. |
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| Authors: | Ding Guang-Tao |
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| Institution: | The College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000, China |
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| Abstract: | A method of constructing canonoid transformations with respect to a Hamiltonian is presented. First, the Hamiltonian system is transformed into a Birkhoffian system. Second, the Birkhoffian system is transformed into a new one under gauge transformation. Finally, the Hamiltonization of new Birkhoffian system is realized. It is pointed out that there exist many different canonoid transformations for one Hamiltonian system. Two examples are given to illustrate the application of the results. |
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| Keywords: | Hamiltonian system canonoid transformation Birkhoffian system gauge transformation |
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