时间尺度上Nabla变分问题的非完整力学系统的Noether理论  

Noether theorem for nonholonomic mechanical systems of Nabla variational problem on time scales

作　　者：祖启航 朱建青[1] ZU Qihang ZHU Jianqing(College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China)

机构地区：[1]苏州科技大学数理学院,江苏苏州215009

出　　处：《中山大学学报（自然科学版）》2017年第1期58-65,共8页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11572212);苏州科技大学研究生科研创新计划(SKCX15_061)

摘　　要：研究了时间尺度上Nabla变分问题的非完整力学系统的Noether理论。根据时间尺度上的微积分理论和Delta导数与Nabla导数之间关系,建立了时间尺度上Nabla导数的非完整Lagrange方程。根据时间尺度上Nabla变分问题的Hamilton作用量在无限小变换下的变换性质,建立了Nabla变分问题的非完整力学系统的Noether等式,并找到了相应的守恒量。最后,举例说明结果的应用。The Noether theorem for nonholonomic mechanical systems of Nabla variational problem on time scales is studied.Firstly,based on the relationship between the Delta calculus and the Nabla calcu-lus on time scales and the theory of time scale,the nonholonomic Lagrange equation for Nabla variational problem on time scales is established.Secondly,according to invariance of the Hamilton action under the infinitesimal transformation of Nabla variational problem on time scales,the Noether identity for nonholo-nomic mechanical systems is established,and the corresponding Noether conserved quantity is obtained. Finally,an example is presented to illustrate the application of the results.

关 键 词：时间尺度 Nabla变分 非完整系统 Noether等式 守恒量 

分 类 号：O316[理学—一般力学与力学基础]