Perturbation Theory of Fractional Lagrangian System and Fractional Birkhoffian System

被引：2
作者：
Song Chuanjing [1 ,2 ]
Zhang Yi [3 ]
机构：
[1] School of Mathematics and Physics,Suzhou University of Science and Technology
[2] College of Science,Nanjing University of Science and Technology
[3] College of Civil Engineering,Suzhou University of Science and Technology
来源：
Transactions of Nanjing University of Aeronautics and Astronautics | 2018年 / 35卷 / 02期
基金：
中国国家自然科学基金;
关键词：
perturbation theory; fractional conservation law; Riemann-Liouville derivative; fractional Euler-Lagrange equation; fractional Birkhoff equation;
D O I：
10.16356/j.1005-1120.2018.02.353
中图分类号：
O316 [分析力学（解析力学）];
学科分类号：
080101 ;
摘要：
Perturbation to symmetry and adiabatic invariants are studied for the fractional Lagrangian system and the fractional Birkhoffian system in the sense of Riemann-Liouville derivatives.Firstly,the fractional Euler-Lagrange equation,the fractional Birkhoff equations as well as the fractional conservation laws for the two systems are listed.Secondly,the definition of adiabatic invariant for fractional mechanical system is given,then perturbation to symmetry and adiabatic invariants are established for the fractional Lagrangian system and the fractional Birkhoffian system under the special and general infinitesimal transformations,respectively.Finally,two examples are devoted to illustrate the results.
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页码：353 / 360
页数：8
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