基于El-Nabulsi分数阶模型的广义Birkhoff系统Noether对称性研究  

Noether symmetries of generalized Birkhoff systems based on El-Nabulsi fractional model

作　　者：张毅[1,2] 丁金凤[3] 

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

出　　处：《南京理工大学学报》2014年第3期409-413,共5页Journal of Nanjing University of Science and Technology

基　　金：国家自然科学基金(10972151;11272227)

摘　　要：为了进一步揭示力学系统的对称性与守恒量之间的内在关系,基于El-Nabulsi分数阶模型提出并研究了广义Birkhoff系统的Noether定理。首先,提出分数阶广义El-Nabulsi-PfaffBirkhoff原理,建立广义El-Nabulsi-Birkhoff方程。其次,基于El-Nabulsi-Pfaff作用量在无限小变换下的不变性,给出广义Birkhoff系统Noether对称性的定义和判据。最后,提出广义Birkhoff系统的Noether定理。该文研究结果可进一步应用于完整和非完整约束系统。To further reveal the inner relationships between the symmetries and conserved quantities of mechanical systems,a Noether＇s theorem of generalized Birkhoff systems is proposed and studied based on El-Nabulsi fractional model. Firstly,a generalized El-Nabulsi-Pfaff-Birkhoff fractional principle is presented, and generalized El-Nabulsi-Birkhoff equations are established; secondly, based on the invariance of the El-Nabulsi-Pfaff action under the infinitesimal transformation,the definitions and criteria of the Noether symmetries of generalized Birkhoff fractional systems are given; finally, a Noether＇s theorem for generalized Birkhoff fractional systems is proposed. The research results may be applied to systems with holonomic or non-holonomic constraints.

关 键 词：力学系统 对称性 守恒量 El-Nabulsi分数阶模型 广义BIRKHOFF系统 NOETHER定理 无限小变换 完整约束系统 非完整约束系统 

分 类 号：O316[理学—一般力学与力学基础]