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XIE Jia-fang, WU Run-heng, ZHANG Zhu, ZOU Jie-tao, LI Guo-fu. Weak Noether symmetry and conserved laws of Birkhoffian systems[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2012, 21(1): 8-12.
Citation: XIE Jia-fang, WU Run-heng, ZHANG Zhu, ZOU Jie-tao, LI Guo-fu. Weak Noether symmetry and conserved laws of Birkhoffian systems[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2012, 21(1): 8-12.

Weak Noether symmetry and conserved laws of Birkhoffian systems

  • Received Date:2011-04-02
  • A new kind of weak Noether symmetry is obtained that arises in the study of Birkhoffian systems. The conserved quantities, which includes Noether conserved quantity, Hojman type conserved quantity and new type conserved quantity, are also calculated from this symmetry. Finally, two examples are presented to illustrated the application of these new results.
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  • [1]
    Santilli R M. Foundations of theoretical mechanicsⅡ[M]. New York: Springer-Verlag, 1983.
    [2]
    Galliullin A S. Analytical dynamics [M]. Moscow: Nauka Press, 1989. (in Russian)
    [3]
    Mei F X, Shi R C, Zhang Y F, et al. Dynamics of the Birkhoffian Systems [M]. Beijing: Beijing Institute of Technology Press, 1996. (in Chinese)
    [4]
    Zhang Y. A set of conserved quantities from Lie symmetries for Birkhoffian systems [J].Acta Phys Sin, 2002, 51(3): 461-464. (in Chinese)
    [5]
    Fu J L, Chen L Q, Xie F P. Perturbation to the symmetries of relativistic Birkhoffian systems and the inverse problems [J].Acta Phys Sin, 2003, 52(11): 2664-2670. (in Chinese)
    [6]
    Zhang Y, Fan C X, Ge W K. A new type of conserved quantities for Birkhoffian systems [J]. Acta Phys Sin, 2004, 53(11): 3644-3647. (in Chinese)
    [7]
    Zhang Y, Feng J. Symmetry and stability of a relativistic Birkhoff system [J].Acta Phys Sin, 2005, 54(7): 2985-2989. (in Chinese)
    [8]
    Xu Z X. Conserved quantity and stability of Birkhoffian system [J]. Acta Phys Sin, 2005,54(10): 4971-4973. (in Chinese)
    [9]
    Zhang P Y, Fang J H. Lie symmetry and non-Noether conserved quantities of variable mass Birkhoffian system [J]. Acta Phys Sin,2006, 55(8): 3813-3816. (in Chinese).
    [10]
    Luo S K, Chen X W, Guo Y X. Theory of symmetry for a rotational relativistic Birkhoff system [J]. Chin Phys, 2002, 11(5): 429-436.
    [11]
    Zhang H B, Gu S L. Lie symmetries and conserved quantities of Birkhoff systems with unilateral constraints [J]. Chin Phys, 2002, 11(8): 765-770.
    [12]
    Luo S K, Cai J L. A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system [J]. Chin Phys, 2003, 12(4): 357-360.
    [13]
    Xu X J, Mei F X, Qin M C. Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system [J]. Chin Phys, 2004, 13(12): 1999-2002.
    [14]
    Mei F X, Gang T Q, Xie J F. A symmetry and a conserved quantity for the Birkhoff system [J]. Chin Phys, 2006, 15(8): 1678-1681.
    [15]
    Xie J F, Gang T Q, Mei F X. Weak Noether symmetry for nonholonomic systems of non-Chetaev’s type [J]. Chin Phys B, 2008, 17(9): 3175-3179.
    [16]
    Jia L Q, Luo S K, Zhang Y Y. Mei symmetry and Mei conserved quantity of Nielsen equation for a nonholonomic system [J]. Acta Phys Sin, 2008, 57(4): 2006-2010. (in Chinese)
    [17]
    Fu J L, Chen L Q, Bai J H. Localized Lie symmetries and conserved quantities for the finite-degree-of-freedom systems [J]. Chin Phys, 2005, 14(1): 6-11.
    [18]
    Fang J H, Ding N, Wang P. A new type of conserved quantity of Mei symmetry for Lagrange system [J]. Chin Phys, 2007, 16(4): 887-890.
    [19]
    Xie J F, Gang T Q, Mei F X. Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems [J].Chin Phys B, 2008, 17(2): 390-393.
    [20]
    Hu C L, Xie J F. A potential integration method for Birkhoffian system [J]. Chin Phys B, 2008, 17(4): 1153-1155.
    [21]
    Cai J L. Conformal invariance and conserved quantities of Mei symmetry for general holonomic systems [J]. Acta Phys Sin, 2009, 58(1): 22-27. (in Chinese)
    [22]
    Ge W K. Mei symmetry and conserved quantity of a holonomic system [J]. Acta Phys Sin, 2008, 57(11): 6714-6717. (in Chinese)
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