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研究增加附加项后广义Hamilton系统的形式不变性及其导出的Mei守恒量. 引进无限小变换群及其生成元向量, 给出增加附加项后广义Hamilton系统的形式不变性的定义和判据, 利用规范函数满足的结构方程, 导出与该系统形式不变性相应的Mei守恒量的表达式. 最后, 给出一个算例, 用于说明结果的应用.
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关键词:
- 附加项 /
- 广义Hamilton系统 /
- 形式不变性 /
- Mei守恒量
Form invariance and Mei conserved quantity for generalized Hamilton systems after adding additional terms are studied. By introducing infinitesimal transformation group and its infinitesimal transformation vector of generators, the definition and determining equations of the Mei symmetry for generalized Hamilton systems after adding additional terms are provided. By means of the structure equation satisfied by the gauge function, the Mei conserved quantity corresponding to the form invariance for the system is derived. Finally an illustrative example is given to verify the results.-
Keywords:
- additional term /
- generalized Hamiltonian system /
- form invariance /
- Mei conserved quantity
[1] Noether A E 1918 Math. Phys. 2 235
[2] Mei F X 1993 Sci. China A 36 1456
[3] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[4] Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[5] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[6] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[7] Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[8] Zheng S W, Zhang Q H, Xie J F 2007 Chin. Phys. Lett. 24 2164
[9] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[10] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[11] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[12] Huang W L, Cai J L 2012 Acta Mech. 223 433
[13] Chen X W, Liu C, Mei F X 2008 Chin. Phys. B 17 3180
[14] Zhang Y Y, Zhang F, Han Y L, Jia LQ 2014 Nonlinear Dyn. 77 521
[15] Jia L Q, Zheng S W 2006 Acta Phys. Sin. 55 3829 (in Chinese) [贾利群, 郑世旺 2006 55 3829]
[16] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[17] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[18] Li L, Luo S k 2013 Acta Mech. 224 1757
[19] Luo S K, Li Z J, Wang P, Li L 2013 Acta Mech. 224 71
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[1] Noether A E 1918 Math. Phys. 2 235
[2] Mei F X 1993 Sci. China A 36 1456
[3] Lou Z M, Mei F X, Chen Z D 2012 Acta Phys. Sin. 61 110204 (in Chinese) [楼智美, 梅凤翔, 陈子栋 2012 61 110204]
[4] Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[5] Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[6] Jia L Q, Sun X T, Zhang M L, Zhang Y Y, Han Y L 2014 Acta Phys. Sin. 63 010201 (in Chinese) [贾利群, 孙现亭, 张美玲, 张耀宇, 韩月林 2014 63 010201]
[7] Fang J H, Zhang B, Zhang W W, Xu R L 2012 Chin. Phys. B 21 050202
[8] Zheng S W, Zhang Q H, Xie J F 2007 Chin. Phys. Lett. 24 2164
[9] Jia L Q, Wang X X, Zhang M L, Han Y L 2012 Nonlinear Dyn. 69 1807
[10] Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[11] Cai J L, Shi S S, Fang H J, Xu J 2012 Meccanica 47 63
[12] Huang W L, Cai J L 2012 Acta Mech. 223 433
[13] Chen X W, Liu C, Mei F X 2008 Chin. Phys. B 17 3180
[14] Zhang Y Y, Zhang F, Han Y L, Jia LQ 2014 Nonlinear Dyn. 77 521
[15] Jia L Q, Zheng S W 2006 Acta Phys. Sin. 55 3829 (in Chinese) [贾利群, 郑世旺 2006 55 3829]
[16] Luo S K, Li L 2013 Nonlinear Dyn. 73 639
[17] Luo S K, Li L 2013 Nonlinear Dyn. 73 339
[18] Li L, Luo S k 2013 Acta Mech. 224 1757
[19] Luo S K, Li Z J, Wang P, Li L 2013 Acta Mech. 224 71
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