时间尺度上近似Hamilton系统的近似Noether对称性  

Approximate Noether Symmetry for Approximate Hamiltonian Systems on Time Scales

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

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

出　　处：《力学季刊》2025年第1期173-180,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12102241);河南省高等学校重点科研基金(20A130003)。

摘　　要：本文利用时间尺度上Noether对称性理论,讨论时间尺度上近似Hamilton系统的近似Noether定理.首先,给出时间尺度上近似Hamilton系统的Hamilton原理,建立了时间尺度上近似Hamilton正则方程.其次,得到时间尺度上近似Hamilton系统的Noether等式,建立时间尺度上近似Noether对称性与近似守恒量之间的联系,得到时间尺度上近似Hamilton系统的近似Noether定理.最后通过算例验证理论结果的应用.In this paper,the approximate Noether theorems for approximate Hamiltonian systems on time scales are investigated based on the Noether symmetry theory on time scales.Firstly,the Hamilton principle for approximate Hamiltonian systems on time scales is presented,and the corresponding approximate Hamilton canonical equations are established.Secondly,the Noether identities for approximate Hamiltonian systems on time scales are derived,and the relationship between approximate Noether symmetry and approximate conserved quantities is established.As a result,the approximate Noether theorems for these systems on time scales are obtained.Finally,an example is provided to demonstrate the application of the theoretical results.

关 键 词：近似Hamilton系统 近似正则方程 近似守恒量 时间尺度 

分 类 号：O316[理学—一般力学与力学基础]