|Table of Contents|

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

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

Issue:
2014年03期
Page:
409-
Research Field:
Publishing date:

Info

Title:
Noether symmetries of generalized Birkhoff systems based on ElNabulsi fractional model
Author(s):
Zhang Yi1; 2; Ding 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
Keywords:
mechanical systems; symmetries; conserved quantities; ElNabulsi fractional model; generalized Birkhoff systems; Noether’s theorem; infinitesimal transformation; holonomic constraint systems; nonholonomic constraint systems
PACS:
O316
DOI:
-
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.

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.

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Last Update: 2014-06-30