弱非完整系统Mei对称性导致的新型精确和近似守恒量

韩月林; 王肖肖; 张美玲; 贾利群

doi:10.7498/aps.62.110201

摘要

研究弱非完整系统Lagrange方程的Mei对称性导致的一种结构方程和新型精确以及近似守恒量. 首先建立系统的Lagrange方程. 其次在群的无限小变换下, 给出了弱非完整系统及其一次近似系统Mei对称性的定义和判据, 然后得到了Mei对称性导致的新型结构方程、新型精确和近似守恒量的表达式. 最后, 举例研究系统的精确新型守恒量和近似新型守恒量问题.

关键词:

A type of structural equation, new exact and approximate conserved quantity which are deduced from Mei symmetry of Lagrange equations for a weakly nonholonomic system, are investigated. First, Lagrange equations of weakly nonholonomic system are established. Next, under the infinitesimal transformations of Lie groups, the definition and the criterion of Mei symmetry for Lagrange equations in weakly nonholonomic systems and its first-degree approximate holonomic system are given. And then, the expressions of new structural equation and new exact and approximate conserved quantities of Mei symmetry for Lagrange equations in weakly nonholonomic systems are obtained. Finelly, an example is given to study the question of the exact and the approximate new conserved quantities.

Keywords:

作者及机构信息

1.
江南大学理学院, 无锡 214122

基金项目: 国家自然科学基金(批准号: 11142014)和江苏省普通高校研究生科研创新计划项目(批准号: CXLX12_0720)资助的课题.

Authors and contacts

1.
School of Science, Jiangnan University, Wuxi 214122, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11142014), and the scientific research and innovation plan for College Graduates of Jiangsu province, China (Grant No. CXLX12_0720).

参考文献

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[2]	Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rat. Mech. Anal. 136 21
[3]	Ostrovskaya S, Angels, 1998 ASME Appl. Mech. Rev. 51 415
[4]	Mei F X 2000 ASME Appl. Mech. Rev. 53 283
[5]	Zegzhda S A, Soltakhanov S K, Yushkov M P 2005 Moscow: FIMATLIT
[6]	Mei F X 1989 Beijing Inst. Technol. 9 10
[7]	Mei F X 1992 Chin. Sci. Bull. 37 1180
[8]	Mei F X 1995 Beijing Inst. Technol. 15 237
[9]	Noether A E 1918 Nachr Akad Wiss Gottingen Math. Phys. Kl 235
[10]	Mei F X 2000 Beijing Inst. Technol. 9 120
[11]	Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[12]	Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[13]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[14]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
[15]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向伟 2010 59 5209]
[16]	Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群 2011 60 111101]
[17]	Cai J L 2012 Nonlinear Dyn. 69 487
[18]	Jia L Q, Wang X X, Zhang M L Han Y L 2012 Nonlinear Dyn. 69 1807
[19]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[20]	Luo S K 2007 Chin. Phys. Lett. 24 2463
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[23]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
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[25]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[26]	Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys. B 18 1731
[27]	Xie Y L, Jia L Q 2010 Chin Phys. Lett. 27 120201
[28]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向伟 2010 59 5209]
[29]	Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[30]	Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽 2011 60 084501]
[31]	Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[32]	Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[33]	Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[34]	Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[35]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[36]	Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 52 1048]
[37]	Zhang Y, Fan C X, Ge W K 2004 Acta Phys. Sin. 53 3644 (in Chinese) [张毅, 范存新, 葛伟宽 2008 53 3644]
[38]	Fang J H, Liu Y K, Zhang X N 2008 Chin. Phys. B 17 1962
[39]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳 2010 59 7552]
[40]	Zhao L, Fu J L, Chen B Y 2011 Chin. Phys. B 20 040201
[41]	Han Y L, Sun X T, Wang X X, Zhang M L, Jia L Q 2012 Chin. Phys. B 21 120201
[42]	Mei F X 2004 Beijing Institute of Technology Press, Beijing

施引文献

[1]	Neimark J I, Fufaev N A 1972 Providence, RI:AMS
[2]	Bloch A M, Krishnaprasad P S, Marsden J E, Murray R M 1996 Arch. Rat. Mech. Anal. 136 21
[3]	Ostrovskaya S, Angels, 1998 ASME Appl. Mech. Rev. 51 415
[4]	Mei F X 2000 ASME Appl. Mech. Rev. 53 283
[5]	Zegzhda S A, Soltakhanov S K, Yushkov M P 2005 Moscow: FIMATLIT
[6]	Mei F X 1989 Beijing Inst. Technol. 9 10
[7]	Mei F X 1992 Chin. Sci. Bull. 37 1180
[8]	Mei F X 1995 Beijing Inst. Technol. 15 237
[9]	Noether A E 1918 Nachr Akad Wiss Gottingen Math. Phys. Kl 235
[10]	Mei F X 2000 Beijing Inst. Technol. 9 120
[11]	Zheng S W, Xie J F, Chen W C 2008 Chin. Phys. Lett. 25 809
[12]	Ge W K 2008 Acta Phys. Sin. 57 6714 (in Chinese) [葛伟宽 2008 57 6714]
[13]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese) [蔡建乐 2009 58 22]
[14]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese) [方建会 2009 58 3617]
[15]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向伟 2010 59 5209]
[16]	Yang X F, Sun X T, Wang X X, Zhang M L, Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese) [杨新芳, 孙现亭, 王肖肖, 张美玲, 贾利群 2011 60 111101]
[17]	Cai J L 2012 Nonlinear Dyn. 69 487
[18]	Jia L Q, Wang X X, Zhang M L Han Y L 2012 Nonlinear Dyn. 69 1807
[19]	Chen X W, Li Y M, Zhao Y H 2005 Phys. Lett. A 337 274
[20]	Luo S K 2007 Chin. Phys. Lett. 24 2463
[21]	Cai J L 2008 Chin. Phys. Lett. 25 1523
[22]	Cai J L, Mei F X 2008 Acta Phys. Sin. 57 5369 (in Chinese) [蔡建乐, 梅凤翔 2008 57 5369]
[23]	Jiang W A, Li Z J, Luo S K 2011 Chin. Phys. B 20 030202
[24]	Xu X J, Mei F X, Qin M C 2004 Acta Phys. Sin. 53 4021 (in Chinese) [许学军, 梅凤翔, 秦茂昌 2004 53 4021]
[25]	Cai J L, Luo S K, Mei F X 2008 Chin. Phys. B 17 3170
[26]	Cui J C, Zhang Y Y, Jia L Q 2009 Chin. Phys. B 18 1731
[27]	Xie Y L, Jia L Q 2010 Chin Phys. Lett. 27 120201
[28]	Zheng S W, Xie J F, Chen X W 2010 Acta Phys. Sin. 59 5209 (in Chinese) [郑世旺, 解加芳, 陈向伟 2010 59 5209]
[29]	Li Y C, Wang X M, Xia L L 2010 Acta Phys. Sin. 59 2935 (in Chinese) [李元成, 王小明, 夏丽莉 2010 59 2935]
[30]	Jia L Q, Sun X T, Zhang M L, Wang X X, Xie Y L 2011 Acta Phys. Sin. 60 084501 (in Chinese) [贾利群, 孙现亭, 张美玲, 王肖肖, 解银丽 2011 60 084501]
[31]	Jiang W A, Luo S K 2012 Nonlinear Dyn. 67 475
[32]	Li Z J, Luo S K 2012 Nonlinear Dyn. 70 1117
[33]	Luo S K, Li Z J, Li L 2012 Acta Mech. 223 2621
[34]	Luo S K, Li Z J, Peng W, Li L 2013 Acta Mech. 224 71
[35]	Han Y L, Wang X X, Zhang M L, Jia L Q 2013 Nonlinear Dyn. 71 401
[36]	Mei F X 2003 Acta Phys. Sin. 52 1048 (in Chinese) [梅凤翔 2003 52 1048]
[37]	Zhang Y, Fan C X, Ge W K 2004 Acta Phys. Sin. 53 3644 (in Chinese) [张毅, 范存新, 葛伟宽 2008 53 3644]
[38]	Fang J H, Liu Y K, Zhang X N 2008 Chin. Phys. B 17 1962
[39]	Jia L Q, Xie Y L, Zhang Y Y, Cui J C, Yang X F 2010 Acta Phys. Sin. 59 7552 (in Chinese) [贾利群, 解银丽, 张耀宇, 崔金超, 杨新芳 2010 59 7552]
[40]	Zhao L, Fu J L, Chen B Y 2011 Chin. Phys. B 20 040201
[41]	Han Y L, Sun X T, Wang X X, Zhang M L, Jia L Q 2012 Chin. Phys. B 21 120201
[42]	Mei F X 2004 Beijing Institute of Technology Press, Beijing

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