时间尺度上广义Chaplygin系统Noether对称性的摄动与绝热不变量  

Perturbation and Adiabatic Invariants of Noether Symmetry for Generalized Chaplygin Systems on Time Scales

作　　者：金世欣 李彦敏 JIN Shixin;LI Yanmin(School of Mathematics and Statistics,Shangqiu Normal University,Shangqiu 476000,Henan,China;School of Physics and Information Engineering,Shangqiu Normal University,Shangqiu 476000,Henan,China)

机构地区：[1]商丘师范学院数学与统计学院,河南商丘476000 [2]商丘师范学院电子电气工程学院,河南商丘476000

出　　处：《力学季刊》2021年第3期550-559,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11572212,11372169);河南省高等学校重点科研基金(20A130003)。

摘　　要：本文研究时间尺度上广义Chaplygin系统的Noether对称性的摄动与绝热不变量.给出时间尺度上广义Chaplygin方程和Noether定理;研究小扰动作用下时间尺度上广义Chaplygin系统的Noether对称性的摄动,得到该系统时间尺度上的一类Noether形式的绝热不变量.并举例说明结果的应用.In this paper,the perturbation and adiabatic invariants of Noether symmetry for generalized Chaplygin systems on time scales are studied.The differential equations of motion and Noether theorems for generalized Chaplygin systems on time scales are given.The perturbation of Noether symmetries for generalized Chaplygin systems on time scales with the action of small disturbance is investigated,and the Noether-type adiabatic invariants for generalized Chaplygin systems on time scales are obtained.An example is given to illustrate the application of the results.

关 键 词：摄动与绝热不变量 广义Chaplygin系统 NOETHER对称性 时间尺度 

分 类 号：O316[理学—一般力学与力学基础]