基于Caputo导数下的含时滞的Hamilton系统的分数阶Noether理论  

Fractional Noether theorems for Hamilton system with time delay based on Caputo dervitaves

作　　者：丁金凤[1] 金世欣[2] 张毅[3] 

机构地区：[1]苏州科技大学数理学院,江苏苏州215009 [2]南京理工大学理学院,江苏南京210094 [3]苏州科技大学土木工程学院,江苏苏州215009

出　　处：《中山大学学报（自然科学版）》2016年第6期79-85,共7页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10972151;11272227)

摘　　要：提出并讨论了Caputo导数定义下的含时滞的Hamilton系统的分数阶Noether对称性与守恒量。根据含时滞的Hamilton系统的分数阶Hamilton原理,建立了相应的含时滞的分数阶Hamilton正则方程;依据分数阶Hamilton作用量在无限小变换下的不变性,得到了含时滞的Hamilton系统的分数阶Noether对称性;最后,建立了系统的含时滞的分数阶Noether理论,并举例说明结果的应用。The fractional Noether symmetries and fractional conserved quantities for Hamilton system with time delay based on Caputo derivatives are discussed.The fractional Hamilton canonical equations of the corresconding system with time delay are established base upon the fractional Hamilton principle of the Hamilton systems with time delay.Then,the fractional Noether symmetries of the Hamilton system with time delay are obtained,which based on the invariance of the fractional Hamilton action with time delay under the infinitesimal transformations of group.Finally,fractional Noether theorems with time delay of the Hamilton system are established.At the end,one example is given to illustrate the application of the results.

关 键 词：时滞 HAMILTON系统 CAPUTO导数 NOETHER对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]