Nabla导数下Hamilton系统的约化

发布时间：2018-03-26 12:35

本文选题：Hamilton系统　切入点：时间尺度　出处：《力学季刊》2017年03期

【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.
[Abstract]:The reduction problem of Hamilton system under nabla derivative is proposed and studied. According to the Hamilton principle of mechanical system under nabla derivative, the canonical equations of Hamilton system are established, the energy integral and cyclic integral of the system are given, and these integrals are used. The results show that the reduced equation still maintains the Hamilton canonical equation form of the system. The reductive theory of the mechanical system under the Nabla derivative is the unification and extension of the reductive theory of the continuous and discrete mechanical systems. In this paper, the reduction of Hamilton system with time scale equal to real number set and integer set is discussed. An example is given to illustrate the application of the result.
【作者单位】：南京理工大学理学院;苏州科技大学土木工程学院;
【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)
【分类号】：O316

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