分数阶Birkhoff系统Noether对称性的摄动与绝热不变量  

Perturbation to Noether Symmetry and Adiabatic Invariants for Fractional Birkhoffian Systems

作　　者：宋传静[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215011

出　　处：《力学季刊》2017年第1期43-49,共7页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11272227;11572212);江苏省高校研究生创新计划项目(KYLX15_0405)

摘　　要：20世纪90年代以来,分数阶微积分理论与方法已被广泛地应用到自然科学和社会科学的各个领域,动力学与控制是其中的一个重要应用领域.为了进一步研究分数阶力学系统,本文基于Riemann-Liouville分数阶导数,讨论了分数阶Birkhoff系统Noether对称性的摄动与绝热不变量问题.首先,给出分数阶Birkhoff系统的运动微分方程及精确不变量;其次,给出绝热不变量的定义,并研究分数阶Birkhoff系统的绝热不变量;文末举例说明结果的应用.Since the 1990s, the theory and method of fractional calculus have been widely applied to various fields of natural science and social science, of which dynamics and control is an important application field. In order to further study the fractional dynamical systems, the perturbation to Noether symmetry and adiabatic invariants for fractional Birkhoffian systems are investigated in this paper based on the Riemann-Liouville fractional derivatives. Firstly, differential equations of motion and exact invariants for fractional Birkhoffian systems are presented. Secondly, the definition of adiabatic invariant is given, and adiabatic invariants for fractional Birkhoffian systems are investigated. And finally, an example is given to demonstrate the application of the results.

关 键 词：Noether对称性摄动 绝热不变量 分数阶Birkhoff系统 Riemann-Liouville分数阶导数 

分 类 号：O316[理学—一般力学与力学基础]