事件空间中一类拟分数阶Birkhoff系统的Noether定理  

Noether’s theorems for a type of quasi-fractional Birkhoffian systems in even space

作　　者：丁金凤[1,2] 张毅 DING Jin-feng;ZHANG Yi(College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou 215009,China;College of Tianpin,Suzhou University of Science and Technology,Suzhou 215009,China;College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]苏州科技大学天平学院,江苏苏州215011 [3]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）》2020年第4期673-678,共6页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11572212,11272227);苏州科技大学天平学院科研基金(TPQN2016003).

摘　　要：基于按指数律拓展的分数阶积分,研究事件空间中拟分数阶Birkhoff系统的Noether对称性与守恒量.首先,基于按指数律拓展的分数阶积分定义,给出事件空间中拟分数阶Pfaff作用量,建立事件空间中拟分数阶Pfaff-Birkhoff原理,并导出Pfaff-Birkhoff-d’Alembert原理,得到事件空间中拟分数阶Birkhoff系统的运动微分方程.其次,计算Pfaff作用量的全变分,给出事件空间中拟分数阶Pfaff作用量的两个变分公式.建立事件空间中拟分数阶Birkhoff系统的Noether对称性的定义和判据.最后,建立事件空间中拟分数阶Birkhoff系统的Noether定理,揭示了系统的Noether对称性与守恒量之间的内在联系.如果分数阶时间积分参数γ=1,则该定理退化为经典的事件空间中Birkhoff系统的Noether定理.文末举例说明结果的应用.Based on the fractional integral extended by exponential law,Noether symmetries and conserved quantities of quasi-fractional Birkhoffian systems in event space have been studied.Firstly,based on the definition of fractional integral extended by exponential law,the quasi-fractional Pfaff action in event space is presented,the quasi-fractional Pfaff-Birkhoff principle in event space is established,and the Pfaff-Birkhoff-d'Alembert principle is derived,and the differential equations of motion for quasi-fractional Birkhoffian systems in event space are obtained.Secondly,the total variation of Pfaff action is calculated,and two variational formulas of quasi-fractional Pfaff action in event space are given.The definition and criterion of Noether symmetry of quasi-fractional Birkhoffian system in event space are established.Finally,Noether’s theorems for quasi-fractional Birkhoffian systems in event space are established which reveal the internal relationship between Noether symmetries and conserved quantities.If the fractional time integral parameter γ=1,the theorems degrade to Noether’s theorems of classical Birkhoffian systems in event space.At the end of the paper,an example is given to illustrate the application of the results.

关 键 词：拟分数阶Birkhoff系统 NOETHER对称性 按指数律拓展的分数阶积分 事件空间 

分 类 号：O316[理学—一般力学与力学基础]