[1]张孝彩,张毅.相空间中基于El-Nabulsi模型的Lie对称性与守恒量(英文)[J].江西师范大学学报(自然科学版),2016,40(01):65-70.
 ZHANG Xiaocai,ZHANG Yi.Lie Symmetry and Conserved Quantity Based on El-Nabulsi Models in Phase Space[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(01):65-70.
点击复制

相空间中基于El-Nabulsi模型的Lie对称性与守恒量(英文)()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年01期
页码:
65-70
栏目:
出版日期:
2016-01-25

文章信息/Info

Title:
Lie Symmetry and Conserved Quantity Based on El-Nabulsi Models in Phase Space
作者:
张孝彩;张毅
1.苏州科技学院数理学院,江苏 苏州 215009; 2.苏州科技学院土木工程学院,江苏 苏州 215011
Author(s):
ZHANG Xiaocai ZHANG Yi
1.College of Mathematics and Physics,Suzhou University of Science and Technology,Suzhou Jiangsu 215009,China; 2.College of Civil Engineering,Suzhou University of Science and Technology,Suzhou Jiangsu 215011,China
关键词:
El-Nabulsi模型 相空间 Lie对称性 广义Hojman守恒量 Noether守恒量
Keywords:
El-Nabulsi models in phase space the Lie symmetry generalized Hojman conserved quantity Noether conserved quantity
分类号:
O 316
文献标志码:
A
摘要:
研究相空间中基于El-Nabulsi非保守动力学模型的Lie对称性与守恒量.首先,建立系统的运动方程.其次,在一般无限小变换下,建立确定方程,从而给出相空间中基于El-Nabulsi模型的Lie对称性的定义和判据,同时,给出相空间中Lie对称性直接导致的广义Hojman守恒量,Hojman守恒量为广义Hojman守恒量一特例.然后,给出基于El-Nabulsi模型的Lie对称性导致的Noether守恒量.最后,给出2个特例说明结果的应用.
Abstract:
In phase space,the Lie symmetry and conserved quantity for non-conservative dynamics based on El-Nabulsi models are studied.Firstly,the differential equations of motion of the systems are established.Secondly,the determining equations are established in phase space under a general infinitesimal transformation,thus the definition and the criterion of Lie symmetry based on El-Nabulsi models are obtained.At the same time,the form of generalized Hojman conserved quantity as a direct result of the Lie symmetry is given in phase space,and the Hojman conserved quantity acts as a special case of the generalized Hojman conserved quantity.Then,the Noether conserved quantity of the Lie symmetry based on El-Nabulsi models is gained.Lastly,two examples are given to illustrate the application of the results.

参考文献/References:

[1] Lutzky M.Dynamical symmetries and conserved quantities [J].Journal of Physics A:Mathematical and General,1979,12(7):973-981.
[2] Zhao Yueyu.Conservative quantities and Lie's symmetries of nonconservative dynamical systems [J].Acta Mechanica Sinica,1994,26(3):380-384.
[3] Mei Fengxiang.Applications of Lie groups and Lie algebras to constrained mechanical systems [M].Beijing: Science Press,1999: 281-379.
[4] Hojman S A.A new conservation law constructed without using either Lagrangians or Hamiltonians [J].Journal of Physics A: Mathematical and General,1992,25(7): 291-295.
[5] Zhang Yi,Xue Yun.Lie symmetries of constrained Hamiltonian system with the second type of constraints [J].Acta Physica Sinica,2001,50(5):816-819.
[6] Zhang Hongbin.Lie symmetries and conserved quantities of non-holonomic mechanical systems with unilateral vacco constraints [J].Chinese Physics,2002,11(1):1-4.
[7] Mei Fengxiang.Lie symmetry and the conserved quantity of a generalized Hamiltonian system [J].Acta Physica Sinica,2003,52(5):1048-1050.
[8] Zhang Yi.A conservation theorem of Hojman for systems of generalized classical mechanics [J].Acta Physica Sinica,2003,52(8):1832-1836.
[9] Zhang Hongbin,Chen Liqun,Liu Rongwan,et al.The generalized Hojman's theorem [J].Acta Physica Sinica,2005,54(6): 2489-2493.
[10] Xie Yinli,Jia Liqun,Luo Shaokai.Special Lie symmetry and Hojman conserved quantity of Appell equations in a dynamical system of relative motion [J].Chinese Physics B,2011,20(1):57-60.
[11] Riewe F.Nonconservative lagrangian and hamiltonian mechanics [J].Physical Review E,1996,53(2):1890-1899.
[12] Klimek M.Fractional sequential mechanics:models with symmetric fractional derivative [J].Czechoslovak Journal of Physics,2001,51(12): 1348-1354.
[13] Agrawal O P.Formulation of Euler-Lagrange equations for fractional variational problems [J].Journal of Mathematical Analysis and Applications,2002,272(1):368-379.
[14] Atanackovic T M,Konjik S,Pilipovic S,et al.Variational problems with fractional derivatives: invariance conditions and Noether's theorem [J].Nonlinear Analysis: Theory,Methods & Applications,2009,71(5):1504-1517.
[15] 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.
[16] El-Nabulsi A R.A fractional approach to nonconservative Lagrangian dynamical systems [J].Fizika A,2005,14(4): 289-298.
[17] El-Nabulsi A R,Torres D F M.Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order(α,β)[J].Mathematical Methods in the Applied Sciences,2007,30(15):1931-1939.
[18] El-Nabulsi A R,Torres D F M.Fractional action-like variational problems [J].Journal of Mathematical Physics,2008,49(5):670-681.
[19] El-Nabulsi A R,Fractional action-like variational problem in holonomic,non-holonomic and semi-holonomic constrained and dissipative dynamical systems [J].Chaos,Solitons and Fractals,2009,42(1): 52-61.
[20] Frederico G S F,Torres D F M.Non-conservative Noether's theorem for fractional action-like variational problems with intrinsic and observer times [J].International Journal of Ecological Economics and Statistics,2007,9(F7): 74-82.
[21] Zhang Yi.Noether symmetry and conserved quantity for a fractional action-like variational problem in phase space [J].Acta Scientiarum Naturalium Universitaties Sunyatseni,2013,52(4): 45-50.
[22] Long Zixuan,Zhang Yi.Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws [J].Chinese Physics B,2014,23(11): 359-367.
[23] Song Chuanjing,Zhang Yi.Conserved quantities and adiabatic invariants for El-Nabulsi's fractional Birkhoff system [J].International Journal of Theoretical Physics,2015,54(8):2481-2493.

备注/Memo

备注/Memo:
基金项目:国家自然科学基金(11272227),江苏省普通高校研究生科研创新计划(KYZZ_0350)和苏州科技学院研究生科研创新计划(SKCX14_058)资助项目.
更新日期/Last Update: 1900-01-01