基于El-Nabulsi分数阶模型的广义Birkhoff系统Noether对称性研究被引量：9

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

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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.

作者张毅丁金凤

机构地区苏州科技学院土木工程学院南京理工大学理学院苏州科技学院数理学院

出处《南京理工大学学报》 EI CAS CSCD 北大核心 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)

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 mechanical systems symmetries conserved quantities El-Nabulsi fractional model generalized Birkhoff systems Noether＇s theorem infinitesimal transformation holonomic constraint systems non-holonomic constraint systems

分类号 O316 [理学—一般力学与力学基础]

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1Riewe F.Nonconservative Lagrangian and Hamiltonian mechanics[J].Physical Review E,1996,53(2):1890-1899.
2Riewe F.Mechanics with fractional derivatives[J].Physical Review E,1997,55(3):3581-3592.
3Agrawal O P.Formulation of EulerLagrange equations for fractional variational problems[J].Journal of Mathematical Analysis and Applications,2002,272(1):368-379.
4Atanackovi 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.
5Malinowska A B,Torres D F M.Introduction to the fractional calculus of variations[M].London,UK:Imperial College Press,2012.
6ElNabulsi A R.A fractional approach to nonconservative Lagrangian dynamical systems[J].Fizika A,2005,14(4):289-298.
7El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.
8ElNabulsi A R,Torres D F M.Fractional actionlike variational problems[J].Journal of Mathematical Physics,2008,49(5):053521.
9El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.
10Herzallah 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.