Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

doi:10.1088/1674-1056/18/11/005

中国物理B ›› 2009, Vol. 18 ›› Issue (11): 4636-4642.doi: 10.1088/1674-1056/18/11/005

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

张毅

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

收稿日期:2008-08-13 修回日期:2008-09-09 出版日期:2009-11-20 发布日期:2009-11-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No10772025) and the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002).

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

Zhang Yi(张毅)^†

College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China

Received:2008-08-13 Revised:2008-09-09 Online:2009-11-20 Published:2009-11-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No10772025) and the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China (Grant No 08KJB130002).

摘要/Abstract

摘要： This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.

Abstract: This paper is devoted to studying the conformal invariance and Noether symmetry and Lie symmetry of a holonomic mechanical system in event space. The definition of the conformal invariance and the corresponding conformal factors of the holonomic system in event space are given. By investigating the relation between the conformal invariance and the Noether symmetry and the Lie symmetry, expressions of conformal factors of the system under these circumstances are obtained, and the Noether conserved quantity and the Hojman conserved quantity directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.

Key words: holonomic system, conformal invariance, symmetry, event space

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.20.Qs (General properties, structure, and representation of Lie groups) 02.40.-k (Geometry, differential geometry, and topology)

张毅. Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space[J]. 中国物理B, 2009, 18(11): 4636-4642.

Zhang Yi(张毅) . Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space[J]. Chin. Phys. B, 2009, 18(11): 4636-4642.

[1]	叶建春, 李俊, 陈晓红, 黄素梅, 欧阳威. Enhancement of corona discharge induced wind generation with carbon nanotube and titanium dioxide decoration[J]. 中国物理B, 2019, 28(9): 95202-095202.
[2]	宋宗斌, 杨雪滢, 封文星, 席忠红, 李烈娟, 石玉仁. Decaying solitary waves propagating in one-dimensional damped granular chain[J]. 中国物理B, 2018, 27(7): 74501-074501.
[3]	王扶刚, 杨阳阳, 韩娟芳, 段文山. Head-on collision between two solitary waves in a one-dimensional bead chain[J]. 中国物理B, 2018, 27(4): 44501-044501.
[4]	杜文青, 孙建安, 杨阳阳, 段文山. Envelope solitary waves and their reflection and transmission due to impurities in a granular material[J]. 中国物理B, 2018, 27(1): 14501-014501.
[5]	崔金超, 刘世兴, 宋端. A necessary and sufficient condition for transforming autonomous systems into linear autonomous Birkhoffian systems[J]. 中国物理B, 2013, 22(10): 104501-104501.
[6]	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.
[7]	张伟伟, 方建会 . Noether–Mei symmetry of discrete mechanico-electrical system[J]. 中国物理B, 2012, 21(11): 110201-110201.
[8]	张克军, 方建会, 李燕. Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system[J]. 中国物理B, 2011, 20(5): 54501-054501.
[9]	王苍龙, 段文山, 陈建敏, 石玉仁. Anisotropic character of atoms in a two-dimensional Frenkel–Kontorova model[J]. 中国物理B, 2011, 20(1): 14601-014601.
[10]	董文山, 黄宝歆, 方建会. Noether's theory of generalized linear nonholonomic mechanical systems[J]. 中国物理B, 2011, 20(1): 10204-010204.
[11]	陶司兴, 夏铁成. The super-classical-Boussinesq hierarchy and its super-Hamiltonian structure[J]. 中国物理B, 2010, 19(7): 70202-070202.
[12]	李元成, 夏丽莉, 王小明. Conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems[J]. 中国物理B, 2009, 18(11): 4643-4649.
[13]	张明江, 方建会, 路凯, 张克军, 李燕. Conformal invariance and conserved quantity of third-order Lagrange equations for non-conserved mechanical systems[J]. 中国物理B, 2009, 18(11): 4650-4656.
[14]	傅景礼, 聂宁明, 黄健飞, Jimé nez Salvador, 唐贻发, Vá zquez Luis, 赵维加. Noether conserved quantities and Lie point symmetries of difference Lagrange--Maxwell equations and lattices[J]. 中国物理B, 2009, 18(7): 2634-2641.
[15]	王鹏, 方建会, 王先明. A generalized Mei conserved quantity and Mei symmetry of Birkhoff system[J]. 中国物理B, 2009, 18(4): 1312-1315.

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

Conformal invariance and Noether symmetry, Lie symmetry of holonomic mechanical systems in event space

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0