A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

doi:10.1088/1674-1056/21/8/080201

中国物理B ›› 2012, Vol. 21 ›› Issue (8): 80201-080201.doi: 10.1088/1674-1056/21/8/080201

• GENERAL • 下一篇

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

崔金超^{a b}, 韩月林^a, 贾利群^a

a School of Science, Jiangnan University, Wuxi 214122, China;
b School of Astronautics, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2012-01-05 修回日期:2012-01-12 出版日期:2012-07-01 发布日期:2012-07-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032).

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

Cui Jin-Chao (崔金超)^{a b}, Han Yue-Lin (韩月林)^a, Jia Li-Qun (贾利群 )^a

a School of Science, Jiangnan University, Wuxi 214122, China;
b School of Astronautics, Beijing Institute of Technology, Beijing 100081, China

Received:2012-01-05 Revised:2012-01-12 Online:2012-07-01 Published:2012-07-01
Contact: Jia Li-Qun E-mail:jlq0000@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032).

摘要/Abstract

摘要： A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied. Under the infinitesimal transformation of groups, from the definition and the criterion of Mei symmetry, a type of structural equation and conserved quantity for the system by proposition 2 are obtained, and the inferences in two special cases are given. Finally, an example is given to illustrate the application of the results.

关键词: Nielsen equation, Mei symmetry, structural equation, conserved quantity

Abstract: A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied. Under the infinitesimal transformation of groups, from the definition and the criterion of Mei symmetry, a type of structural equation and conserved quantity for the system by proposition 2 are obtained, and the inferences in two special cases are given. Finally, an example is given to illustrate the application of the results.

Key words: Nielsen equation, Mei symmetry, structural equation, conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

11.30.-j (Symmetry and conservation laws) 45.20.Jj (Lagrangian and Hamiltonian mechanics)

崔金超, 韩月林, 贾利群 . A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system[J]. 中国物理B, 2012, 21(8): 80201-080201.

Cui Jin-Chao (崔金超), Han Yue-Lin (韩月林), Jia Li-Qun (贾利群 ). A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system[J]. Chin. Phys. B, 2012, 21(8): 80201-080201.

参考文献 24

[1]	Bloch A M, Baillieul J, Crouch P and Marsden J 2003 Nonholonomic Mechanics and Control (London: Springer)
[2]	Vagner V V 1941 Trndy Sem. Vektor. Tenzor. Anal. 5 173 (in Russian)
[3]	Etayo F, Santamaria R and Vacaru S I 2005 J. Math. Phys. 46 032901
[4]	Bloch A M, Krishnaprasad P S, Marsden J E and Murray R M 1996 Arch. Rat. Mech. Anal. 136 21
[5]	Mei F X 1991 Advanced Analytical Mechanics (Beijing: Beijing Institute of Technology Press) (in Chinese)
[6]	Luo S K 2007 Acta Phys. Sin. 56 5580 (in Chinese)
[7]	Cai J L 2010 Chin. J. Phys. 48 728
[8]	Jiang W A, Li L, Li Z J and Luo S K 2012 Nonlinear Dynam. 67 1075
[9]	Jia L Q, Xie Y L, Zhang Y Y and Yang X F 2010 Chin. Phys. B 19 110301
[10]	Zhang Y and Mei F X 2000 Chin. Sci. Bull. 45 135
[11]	Cai J L 2010 Int. J. Theor. Phys. 49 201
[12]	Cui J C, Jia L Q and Zhang Y Y 2009 Commun. Theor. Phys. 52 7
[13]	Jiang W A and Luo S K 2012 Nonlinear Dynam. 67 475
[14]	Cai J L 2008 Acta Phys. Sin. 57 5369 (in Chinese)
[15]	Li Z J, Jiang W A and Luo S K 2012 Nonlinear Dynam. 67 445
[16]	Yang X F, Sun X T, Wang X X, Zhang M L and Jia L Q 2011 Acta Phys. Sin. 60 111101 (in Chinese)
[17]	Cui J C, Zhang Y Y and Jia L Q 2009 Chin. Phys. B 18 1731
[18]	Jiang W A and Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese)
[19]	Wang S Y and Mei F X 2001 Chin. Phys. 10 373
[20]	Fang J H, Xue Q Z and Zhao S Q 2002 Acta Phys. Sin. 51 2183 (in Chinese)
[21]	Cai J L 2009 Acta Phys. Sin. 58 22 (in Chinese)
[22]	Xie Y L, Jia L Q and Yang X F 2011 Acta Phys. Sin. 60 030201 (in Chinese)
[23]	Fang J H 2009 Acta Phys. Sin. 58 3617 (in Chinese)
[24]	Xu X J, Mei F X and Qin M C 2004 Acta Phys. Sin. 53 4021 (in Chinese)

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

A type of conserved quantity of Mei symmetry of Nielsen equations for a holonomic system

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 24

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Jian Zhang(张健), Yiming Liu(刘一鸣), and Zhanchun Tu(涂展春). Exploring fundamental laws of classical mechanics via predicting the orbits of planets based on neural networks[J]. 中国物理B, 2022, 31(9): 94502-094502.
[2]	宋静, 张毅. Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales[J]. 中国物理B, 2017, 26(8): 84501-084501.
[3]	王琳莉, 傅景礼. Non-Noether symmetries of Hamiltonian systems withconformable fractional derivatives[J]. 中国物理B, 2016, 25(1): 14501-014501.
[4]	夏丽莉, 陈立群, 傅景礼, 吴旌贺. Symmetries and variational calculationof discrete Hamiltonian systems[J]. , 2014, 23(7): 70201-070201.
[5]	吴越, 胡勇, 何小海, 邓垦. Impact of user influence on information multi-step communication in micro-blog[J]. 中国物理B, 2014, 23(6): 60101-060101.
[6]	金世欣, 张毅. Noether symmetry and conserved quantity for a Hamilton system with time delay[J]. 中国物理B, 2014, 23(5): 54501-054501.
[7]	周燕, 张毅. Noether's theorems of a fractional Birkhoffian system within Riemann–Liouville derivatives[J]. 中国物理B, 2014, 23(12): 124502-124502.
[8]	孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.
[9]	赵纲领, 陈立群, 傅景礼, 洪方昱. Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices[J]. 中国物理B, 2013, 22(3): 30201-030201.
[10]	陈蓉, 许学军. Conformal invariance, Noether symmetry, Lie symmetry and conserved quantities of Hamilton systems[J]. 中国物理B, 2012, 21(9): 94501-094501.
[11]	张斌, 方建会, 张伟伟 . Symmetry of Lagrangians of holonomic nonconservative system in event space[J]. 中国物理B, 2012, 21(7): 70208-070208.
[12]	夏丽莉, 陈立群. Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices[J]. 中国物理B, 2012, 21(7): 70202-070202.
[13]	王鹏, 薛纭, 刘宇陆 . Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics[J]. 中国物理B, 2012, 21(7): 70203-070203.
[14]	贾利群, 张美玲, 王肖肖, 韩月林 . Form invariance and approximate conserved quantity of Appell equations for a weakly nonholonomic system[J]. 中国物理B, 2012, 21(7): 70204-070204.
[15]	吴惠彬, 梅凤翔. Symmetry of Lagrangians of a holonomic variable mass system[J]. 中国物理B, 2012, 21(6): 64501-064501.