分数阶广义Birkhoff系统的Mei对称性及其守恒量  

Mei symmetry and conserved quantity for fractional generalized Birkhoffian systems

作　　者：王璐 张毅[2] WANG Lu;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4期846-854,共9页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(11972241);江苏省自然科学基金(BK20191454);江苏省研究生科研创新计划(KYCX21_3002).

摘　　要：研究分数阶广义Birkhoff系统的对称性和守恒律.首先,根据分数阶广义Pfaff-Birkhoff原理,建立分数阶广义Birkhoff系统的运动微分方程;其次,基于动力学函数在经历群的无限小变换后仍然满足原方程的不变性,给出分数阶广义Birkhoff系统的Mei对称性的定义和判据方程;再次,建立并证明该系统的Mei对称性定理,给出分数阶Mei守恒量.整数阶广义Birkhoff系统、分数阶Birkhoff系统和分数阶Hamilton系统Mei对称性定理是其特例,最后举例以说明定理的应用.The symmetry and conserved quantity for fractional generalized Birkhoffian systems are studied.Firstly,the fractional generalized Birkhoff’s equations are established according to the fractional generalized Pfaff-Birkhoff principle.Secondly,the definition and the determining equation of Mei symmetry of fractional Birkhoffian system are established based on the fact that the dynamics function in the dynamics equation still satisfies the invarianceof the original equation after undergoing infinitesimal transformation of the group.Thirdly,Mei symmetry theorems of the system are given and proved,and fractional Mei conserved quantity is obtained.The Mei symmetry theorems of integer order generalized Birkhoffian system,fractional Birkhoffian system and fractional Hamiltonian system are special cases.Finally,an example is given to illustrate the application of the theorems.

关 键 词：分数阶微积分 广义BIRKHOFF系统 MEI对称性 MEI守恒量 

分 类 号：O316[理学—一般力学与力学基础]