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微扰Kepler系统的守恒量与对称性
引用本文:楼智美,葛伟宽.微扰Kepler系统的守恒量与对称性[J].动力学与控制学报,2009,7(4):313-317.
作者姓名:楼智美  葛伟宽
作者单位:1. 绍兴文理学院物理系,绍兴,312000
2. 湖州师范学院理学院,湖州,313000
摘    要:用直接积分法和Noether法研究微扰Kepler系统的守恒量,都得到了一个不同于Hamilton函数的守恒量,此守恒量与Runge—Lenz矢量有相同的量纲,可以称其为“类Runge-Lenz矢量守恒量”.文中还讨论了守恒量的Noether对称性、Lie对称性与Mei对称性,结果表明:与守恒量相应的无限小变换同时是Noether对称变换、Lie对称变换和Mei对称变换.

关 键 词:微扰Kepler系统  直接积分法  Noether法  守恒量  Noether对称性  Lie对称性  Mei对称性
收稿时间:2009/3/13 0:00:00
修稿时间:2009/4/11 0:00:00

The conserved quantity and symmetry of perturbed kepler system
Lou Zhimei and Ge Weikuan.The conserved quantity and symmetry of perturbed kepler system[J].Journal of Dynamics and Control,2009,7(4):313-317.
Authors:Lou Zhimei and Ge Weikuan
Institution:Lou Zhimei1 Ge Weikuan2(1.Department of Physics,Shaoxing College of Arts , Sciences,Shaoxing 312000,China)(2.School of Science,Huzhou Teachers College,Huzhou 313000,China)
Abstract:The conserved quantity of the perturbed Kepler system was studied by using the direct integral method and Noether method. One conserved quantity ,different from the Hamiltonian,was obtained by two different methods.The dimension of the conserved quantity is identical with the Runge-Lenz vector's ,so we can name this conserved quantity analogous Runge-Lenz vector conserved quantity. Furthermore,the Noether symmetry,the Lie symmetry and the Mei symmetry of the conserved quantity were also discussed. The resea...
Keywords:perturbed Kepler system  direct integral method  Noether method  conserved quantity  Noether symmetry  Lie symmetry  Mei symmetry  
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