时间尺度上非迁移Birkhoff系统的Mei对称性定理  

Mei’s symmetry theorems for non-migrated Birkhoffian systems on a time scale

作　　者：张毅[1] Zhang Yi(College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215011,China)

机构地区：[1]苏州科技大学土木工程学院,苏州215011

出　　处：《物理学报》2021年第24期184-192,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11972241,11572212);江苏省自然科学基金(批准号:BK20191454)资助的课题.

摘　　要：研究并证明时间尺度上非迁移Birkhoff系统的Mei对称性定理.首先,建立任意时间尺度上Pfaff-Birkhoff原理和广义Pfaff-Birkhoff原理,由此导出时间尺度上非迁移Birkhoff系统(包括自由Birkhoff系统、广义Birkhoff系统和约束Birkhoff系统)的动力学方程.其次,基于非迁移Birkhoff方程中的动力学函数经历变换后仍满足原方程的不变性,给出了时间尺度上Mei对称性的定义,导出了相应的判据方程.再次,建立并证明了时间尺度上非迁移Birkhoff系统的Mei对称性定理,得到了时间尺度上Birkhoff系统的Mei守恒量.并通过3个算例说明了结果的应用.The Mei symmetry and its corresponding conserved quantities for non-migrated Birkhoffian systems on a time scale are proposed and studied. Firstly, the dynamic equations of non-migrated Birkhoffian systems(including free Birkhoffian systems, generalized Birkhoffian systems and constrained Birkhoffian systems) on a time scale are derived based on the time-scale Pfaff-Birkhoff principle and time-scale generalized Birkhoff principle. Secondly, based on the fact that the dynamical functions in the non-migrated Birkhoff’s equations still satisfy the original equations after they have been transformed, the definitions of Mei symmetry on an arbitrary time scale are given, and the corresponding criterion equations are derived. Thirdly, Mei’s symmetry theorems for non-migrated Birkhoffian systems on a time scales are established and proved, and Mei conserved quantities of Birkhoffian systems on a time scale are obtained. The results are illustrated by three examples.

关 键 词：BIRKHOFF系统 Mei对称性定理 时间尺度 非迁移变分学 

分 类 号：O175[理学—数学]