文献类型：期刊文献

中文题名：二维各向异性谐振子的第三个独立守恒量及其对称性

英文题名：The third independent conserved quantity and its symmetry of the two-dimensional anisotropic harmonic oscillator

作者：楼智美[1];梅凤翔[2]

机构：[1]绍兴文理学院物理系;[2]北京理工大学力学系

年份：2012

卷号：61

期号：11

起止页码：21

中文期刊名：物理学报

外文期刊名：Acta Physica Sinica

收录：SCI-EXPANDED(收录号：WOS:000305377400002)、CSTPCD、、北大核心2011、Scopus、CSCD2011_2012、WOS、北大核心、CSCD

基金：Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 10932002).

语种：中文

中文关键词：扩展Prelle-Singer法;二维各向异性谐振子;守恒量;对称性

外文关键词：extended P-S method;two-dimensional anisotropic harmonic oscillator;conserved quantity;symmetry

中文摘要：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.

外文摘要：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.