基于非标准Lagrange函数的分数阶Lagrange系统的Noether对称性与守恒量  

Noether symmetry and conserved quantities of fractional Lagrange systems based on non-standard Lagrangians

作　　者：张林洁 张毅[2] ZHANG Lin-jie;ZHANG Yi(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou 215009,Jiangsu,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009 [2]苏州科技大学土木工程学院,江苏苏州215011

出　　处：《云南大学学报（自然科学版）》2023年第1期82-90,共9页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11972241,11572212,11272227);江苏省自然科学基金(BK20191454)。

摘　　要：研究基于两类非标准Lagrange函数(指数Lagrange函数和幂律Lagrange函数)的分数阶Lagrange系统的Noether对称性与守恒量.首先,分别导出Caputo分数阶导数下两类非标准Lagrange系统的运动微分方程;其次,根据作用量在无穷小变换下的不变性,给出了分数阶非标准Lagrange系统的Noether对称变换的定义和判据;最后,建立系统的Noether定理并举例说明结果的应用.The Noether symmetry and conserved quantities of fractional Lagrange systems based on two kinds of non-standard Lagrangians(i.e.,exponential Lagrangian and power-law Lagrangian)are studied.Firstly,the differential equations of motion for two kinds of non-standard Lagrange systems with Caputo fractional derivatives are derived respectively.Secondly,according to the invariance of the action under the infinitesimal transformations,the definitions and criterions of Noether symmetric transformations for fractional non-standard Lagrange systems are given.Finally,Noether’s theorems are established and two examples are given to illustrate the application of the results.

关 键 词：分数阶Lagrange系统 非标准Lagrange函数 NOETHER对称性 CAPUTO导数 

分 类 号：O316[理学—一般力学与力学基础]