Nabla导数下Hamilton系统的约化  

Reduction for Hamilton System with Nabla Derivatives

作　　者：金世欣[1] 张毅[2] 

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

出　　处：《力学季刊》2017年第3期447-457,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11572212;11272227);江苏省研究生培养创新工程(KYLX16_0414)

摘　　要：提出并研究nabla导数下Hamilton系统的约化问题.依据nabla导数下力学系统的Hamilton原理,建立Hamilton系统的正则方程,给出系统的能量积分和循环积分;并利用这些积分,约化系统的Hamilton正则方程.结果表明:约化后的方程仍保持系统的Hamilton正则方程形式,Nabla导数下力学系统的约化理论是连续和离散力学系统的约化理论的统一和拓展.文中讨论了时间尺度等于实数集和整数集两种特殊情形下Hamilton系统的约化,并举例说明了结果的应用.The reduction for Hamilton system with nabla derivatives is proposed and studied. The canonical equations of Hamilton system are established based on the Hamilton principle of mechanical system. The cyclic integrals and the energy integral of the system are given. The canonical equations of the system are reduced by using the energy integral and the cyclic integrals. The results show that the reduced equations hold the form of Hamilton canonical equations for the system with nabla derivatives. The reduction of mechanical system with nabla derivatives is the unification and extension of the reduction theory for the continuum and discrete systems. Two special cases of the reduction of Hamilton systems, in which the time scales are equal to the set of real numbers and the integers, are discussed. Finally, two examples are given to illustrate the application of the results.

关 键 词：HAMILTON系统 时间尺度 约化 循环积分 能量积分 

分 类 号：O316[理学—一般力学与力学基础]