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

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.