| 二维各向异性谐振子的第三个独立守恒量及其对称性 |
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| 引用本文： | 楼智美,梅凤翔.二维各向异性谐振子的第三个独立守恒量及其对称性[J].物理学报,2012,61(11):110201-110201. |
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| 作者姓名： | 楼智美 梅凤翔 |
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| 作者单位： | 1. 绍兴文理学院物理系,绍兴,312000
2. 北京理工大学力学系,北京,100081 |
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| 基金项目： | 国家自然科学基金重点项目(批准号: 10932002) 资助的课题. |
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| 摘 要： | 二维各向异性谐振子和两分振子的能量是守恒的, 但三个守恒量中只有其中两个是独立的. 当频率比ω1/ω2 为有理数时, 系统存在第三个独立的守恒量.本文用扩展Prelle-Singer 法得到五个典型谐振子的第三个独立守恒量, 并讨论了与守恒量相应的Noether对称性与Lie对称性.
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| 关 键 词： | 扩展Prelle-Singer法 二维各向异性谐振子 守恒量 对称性 |
| 收稿时间： | 2011-06-19 |
The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator |
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| Lou Zhi-Mei,Mei Feng-Xiang.The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator[J].Acta Physica Sinica,2012,61(11):110201-110201. |
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| Authors: | Lou Zhi-Mei Mei Feng-Xiang |
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| Institution: | 1. Department of Physics, Shaoxing University, Shaoxing 312000, China;2. Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | The energy and the two partial energies of two-dimensional anisotropic harmonic oscillator are conserved quantities,but only two of them are independent.The system possesses the third independent conserved quantity when the ω1/ω2 is a rational number.The extended Prelle-Singer method is used to find the third independent conserved quantity for the five typical two-dimensional anisotropic harmonic oscillators.The Noether symmetry and the Lie symmetry of the third independent conserved quantities are also discussed. |
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| Keywords: | extended P-S method two-dimensional anisotropic harmonic oscillator conserved quantity symmetry |
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