[1]张毅,丁金凤.基于ElNabulsi分数阶模型的广义Birkhoff系统Noether对称性研究[J].南京理工大学学报(自然科学版),2014,38(03):409.
 Zhang Yi,Ding Jinfeng.Noether symmetries of generalized Birkhoff systems based on ElNabulsi fractional model[J].Journal of Nanjing University of Science and Technology,2014,38(03):409.
点击复制

基于ElNabulsi分数阶模型的广义Birkhoff系统Noether对称性研究
分享到:

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

卷:
38卷
期数:
2014年03期
页码:
409
栏目:
出版日期:
2014-06-30

文章信息/Info

Title:
Noether symmetries of generalized Birkhoff systems based on ElNabulsi fractional model
作者:
张毅12丁金凤3
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
Author(s):
Zhang Yi12Ding Jinfeng3
1.College of Civil Engineering,Suzhou University of Science and Technology,Suzhou 215009,China; 2.School of Sciences,NUST,Nanjing 210094,China;3.College of Mathematics and Physics, Suzhou University of Science and Technology,Suzhou 215009,China
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
Keywords:
mechanical systemssymmetriesconserved quantitiesElNabulsi fractional modelgeneralized Birkhoff systemsNoether’s theoreminfinitesimal transformationholonomic constraint systemsnonholonomic constraint systems
分类号:
O316
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PfaffBirkhoff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
Abstract:
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.

参考文献/References:

[1]Riewe F.Nonconservative Lagrangian and Hamiltonian mechanics[J].Physical Review E,1996,53(2):1890-1899.
[2]Riewe F.Mechanics with fractional derivatives[J].Physical Review E,1997,55(3):3581-3592.
[3]Agrawal O P.Formulation of EulerLagrange equations for fractional variational problems[J].Journal of Mathematical Analysis and Applications,2002,272(1):368-379.
[4]Atanackovi T M,Konjik S,Pilipovi S et al.Variational problems with fractional derivatives:Invariance conditions and Nther’s theorem[J].Nonlinear Analysis:Theory,Methods and Applications,2009,71(5-6):1504-1517.
[5]Malinowska A B,Torres D F M.Introduction to the fractional calculus of variations[M].London,UK:Imperial College Press,2012.
[6]ElNabulsi A R.A fractional approach to nonconservative Lagrangian dynamical systems[J].Fizika A,2005,14(4):289-298.
[7]ElNabulsi A R.Necessary optimality conditions for fractional actionlike integrals of variational calculus with RiemannLiouville fractional derivatives of order(α,β)[J].Mathematical Methods in the Applied Sciences,2007,30(15):1931-1939.
[8]ElNabulsi A R,Torres D F M.Fractional actionlike variational problems[J].Journal of Mathematical Physics,2008,49(5):053521.
[9]ElNabulsi A R.Fractional actionlike variational problems in holonomic,nonholonomic and semiholonomic constrained and dissipative dynamical systems[J].Chaos,Solitons & Fractals,2009,42(1):52-61.
[10]Herzallah M A E,Muslih S I,Baleanu D,et al.HamiltonJacobi and fractional like action with time scaling[J].Nonlinear Dynamics,2011,66(4):549-555.
[11]Frederico G S F,Torres D F M.Constants of motion for fractional actionlike variational problems[J].International Journal of Applied Mathematics,2006,19(1):97-104.
[12]Frederico G S F,Torres D F M.Nonconservative Noether’s theorem for fractional actionlike variational problems with intrinsic and observer times[J].International Journal of Ecological Economics and Statistics,2007,9(F07):74-82.
[13]Zhang Yi,Zhou Yan.Symmetries and conserved quantities for fractional actionlike Pfaffian variational problems[J].Nonlinear Dynamics,2013,73(1-2):783-793.
[14]梅凤翔.广义Birkhoff系统动力学[M].北京:科学出版社,2013.

备注/Memo

备注/Memo:
收稿日期:2013-05-02修回日期:2013-05-21
基金项目:国家自然科学基金(10972151;11272227)
作者简介:张毅(1964-),男,教授,博士生导师,主要研究方向:力学中的数学方法,E-mail:zhy@mail.usts.edu.cn。
引文格式:张毅,丁金凤.基于ElNabulsi分数阶模型的广义Birkhoff系统Noether对称性研究[J].南京理工大学学报,2014,38(3):409-413.
投稿网址:http://zrxuebao.njust.edu.cn
更新日期/Last Update: 2014-06-30