离散Kepler系统的共形不变性与守恒量  

Conformal Invariance and Conserved Quantity of Discrete Kepler Systems

作　　者：夏丽莉[1,2] 张伟 XIA Lili;ZHANG Wei(College of Mechanical Engineering and Applied Electronics Technology,Beijing University of Technology,Beijing 100124,China;College of Physical and Electronic Engineering, Henan Institute of Finance and Banking,Zhengzhou 450046,China)

机构地区：[1]北京工业大学机械工程与应用电子技术学院,北京100124 [2]河南财政金融学院物理与电子工程学院,河南郑州450046

出　　处：《郑州大学学报（理学版）》2018年第1期86-89,共4页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金项目(11502071;11290152);北京市朝阳区博士后基金项目(2016ZZ-01-17);河南省高等学校重点项目(17A140015)

摘　　要：研究了离散Kepler系统的Lie对称性共形不变性和Noether守恒量,得到了Kepler系统的差分方程和能量演化方程,给出系统的共形不变性定义和共形因子,得到系统的共形不变性是Lie对称性的充要条件.讨论离散Kepler系统的Lie对称性和共形不变性之间的关系,给出系统的离散Noether定理,利用离散变分算法模拟系统的守恒量.The conformal invariance of the Lie symmetry and the Noether conserved quantities were investigated for discrete Kepler systems.The difference equations and the energy equations of the Kepler systems were obtained.The conformal invariance of the Lie symmetry and the conformal factor were defined for the systems.The necessary and sufficient conditions of the Lie symmetries being the conformal symmetries were proposed.The relations between the Lie symmetries and the conformal invariance were discussed.The Noether theorems of the systems were derived.An example was given to illustrate the application of the results.

关 键 词：离散Kepler系统 离散Noether定理 Lie对称性共形不变性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]