广义算子下约束Hamilton系统的Noether定理  

Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators

作　　者：沈世磊 宋传静[1] SHEN Shilei;SONG Chuanjing(School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou,Jiangsu 215009,P.R.China)

机构地区：[1]苏州科技大学数学科学学院,江苏苏州215009

出　　处：《应用数学和力学》2022年第12期1422-1433,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12172241,12272248,11972241,11802193);江苏省自然科学基金(BK20191454);江苏省高校“青蓝工程”项目。

摘　　要：研究了广义算子下奇异系统的Noether对称性与守恒量.首先,建立了广义算子下奇异系统的Lagrange方程,并导出该系统的初级约束,然后引入Lagrange乘子建立了广义算子下约束Hamilton方程以及相容性条件.其次,基于Hamilton作用量在无限小变换下的不变性,建立了广义算子下约束Hamilton系统的Noether定理,并给出了该系统的对称性及相应的守恒量.在特定条件下,广义算子下约束Hamilton系统的Noether守恒量可以退化为整数阶约束Hamilton系统的Noether守恒量.最后举例说明了结果的应用.Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied.Firstly,the Lagrangian equation of singular systems under generalized operators was established,and the primary constraints on the system were derived.Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators.Secondly,based on the invariance of the Hamilton action under the infinitesimal transformation,Noether’s theorem for constrained Hamiltonian systems under generalized operators was established,and the symmetry and corresponding conserved quantity of the system were given.Under certain conditions,Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems.Finally,an example illustrates the application of the results.

关 键 词：广义算子 奇异系统 初级约束 约束Hamilton方程 NOETHER定理 对称性与守恒量 

分 类 号：O316[理学—一般力学与力学基础]