时间尺度上Lagrange系统对称性摄动与绝热不变量  

Perturbation to symmetry and adiabatic invariant for Lagrangian system on time scale

作　　者：宋传静[1] 张毅[1,2] Song Chuanjing Zhang Yi(School of Science,Nanjing University of Science and Technology, Nanjing 210094 , China College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[1]南京理工大学理学院,江苏南京210094 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《南京理工大学学报》2017年第2期181-185,共5页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(11272227;11572212);江苏省高校研究生创新计划(KYLX15_0405)

摘　　要：为了揭示小扰动作用下对称性的改变与其不变量之间的内在关系,该文研究了时间尺度上Lagrange系统的Noether对称性摄动与绝热不变量问题。给出了时间尺度上Lagrange系统的运动微分方程、Noether对称性与精确不变量,还给出了绝热不变量的定义,研究了时间尺度上Lagrange系统的绝热不变量。最后举例说明了结果的应用,证明了该文方法及结果的适用性。In order to reveal the internal relationships between the symmetry change and the invariant under the small disturbance, the perturbation to the Noether symmetry and adiabatic invariants for Lagrangian systems on time scales are studied in this paper. The differential equations of motion, the Noether symmetry and exact invariant for Lagrangian systems on time scales are presented. The definition of the adiabatic invariant on time scales is given, and the perturbation to the Noether symmetry and adiabatic invariants for Lagrangian systems on time scales are investigated. Finally,an example is given to illustrate the method and results.

关 键 词：对称性摄动 绝热不变量 LAGRANGE系统 时间尺度 

分 类 号：O316[理学—一般力学与力学基础]