| 弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量 |
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| 引用本文： | 楼智美,梅凤翔,陈子栋.弱非线性耦合二维各向异性谐振子的一阶近似Lie对称性与近似守恒量[J].物理学报,2012,61(11):110204-110204. |
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| 作者姓名： | 楼智美 梅凤翔 陈子栋 |
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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： | 用近似Lie对称性理论研究弱非线性耦合二维各向异性 谐振子的一阶近似Lie对称性与近似守恒量, 并以频率比为2:1的弱非线性耦合二维各向异性谐振子为例, 得到其6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1 个一阶近似守恒量为稳定的一阶近似守恒量.
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| 关 键 词： | 弱非线性耦合二维各向异性谐振子 近似Lie对称性 近似守恒量 |
| 收稿时间： | 2011-07-30 |
The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator |
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| Lou Zhi-Mei,Mei Feng-Xiang,Chen Zi-Dong.The first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator[J].Acta Physica Sinica,2012,61(11):110204-110204. |
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| Authors: | Lou Zhi-Mei Mei Feng-Xiang Chen Zi-Dong |
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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 first-order approximate Lie symmetries and approximate conserved quantities of the weak nonlinear coupled two-dimensional anisotropic harmonic oscillator are studied. When the ω1/ω2 is equal to 2/1, the system possesses six first-order approximate Lie symmetries and approximate conserved quantities, one of them is an exact conserved quantity, four of them are trivial conserved quantities, only one of them is a stable conserved quantity. |
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| Keywords: | weak nonlinear coupled two-dimensional anisotropic harmonic oscillator approximate Lie symmetries approximate conserved quantity |
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