相空间中含时滞的非保守力学系统的Noether定理  

Noether Theorem for Nonconservative Mechanical System with Time Delay in Phase Space

作　　者：金世欣[1] 张毅[2] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215009 [2]苏州科技学院土木工程学院,江苏苏州215009

出　　处：《中山大学学报（自然科学版）》2014年第4期56-61,共6页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10972151;11272227);苏州科技学院研究生科研创新计划资助项目(SKCX12S-039)

摘　　要：研究相空间中含时滞的非保守力学系统的Noether对称性与守恒量。建立含时滞的非保守系统动力学的Hamilton正则方程;依据相空间中含时滞的Hamilton作用量在无限小群变换下的广义准不变性,给出相空间中含时滞的Noether广义准对称变换的定义和判据;并建立相空间中含时滞的非保守力学系统的Noether对称性与守恒量之间的联系。文末,举例说明结果的应用。The Noether symmetries and the conserved quantities for nonconservative mechanical systems with time delay in phase space are studied .Firstly, the Hamilton canonical equations with time delays for the non-conservative systems are established .Secondly , according to the generalized quasi-invariance of the Hamilton action with time delay in phase space under the infinitesimal transformations of groups , the definitions and criterion of the Noether generalized quasi-symmetric transformations with time delay in phase space are given .Lastly, the relationship between the Noether symmetries and the conserved quanti-ties with time delay in phase space are established .At the end , an example is given to illustrate the ap-plication of the results .

关 键 词：非保守系统 NOETHER对称性 时滞 相空间 守恒量 

分 类 号：O316[理学—一般力学与力学基础]