Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

doi:10.1088/1674-1056/22/3/030201

中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/22/3/030201

• GENERAL • 下一篇

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

赵纲领^{a b d}, 陈立群^{a b}, 傅景礼^c, 洪方昱^c

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mechanics, Shanghai University, Shanghai 200444, China;
c Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;
d Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China

收稿日期:2012-06-17 修回日期:2012-08-07 出版日期:2013-02-01 发布日期:2013-02-01
基金资助:
Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209), the National Natural Science Foundation of China (Grant No. 11072218), and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110314).

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

Zhao Gang-Ling (赵纲领)^{a b d}, Chen Li-Qun (陈立群)^{a b}, Fu Jing-Li (傅景礼)^c, Hong Fang-Yu (洪方昱)^c

a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Mechanics, Shanghai University, Shanghai 200444, China;
c Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China;
d Department of Physics and Information Engineering, Shangqiu Normal University, Shangqiu 476000, China

Received:2012-06-17 Revised:2012-08-07 Online:2013-02-01 Published:2013-02-01
Contact: Fu Jing-Li E-mail:sqfujingli@163.com
Supported by:
Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209), the National Natural Science Foundation of China (Grant No. 11072218), and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110314).

摘要/Abstract

摘要： In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced on the regular and rregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for applications of the results.

关键词: regular and irregular lattice, nonholonomic system, Noether symmetry, Mei symmetry

Abstract: In this paper, Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated. Firstly, the equations of motion of discrete nonholonomic systems are introduced on the regular and rregular lattices. Secondly, for cases of the two lattices, based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates, we present the quasi-extremal equation, the discrete analogues of Noether identity, Noether theorems, and the Noether conservation laws of the systems. Thirdly, in cases of the two lattices, we study the Mei symmetry in which we give the discrete analogues of the criterion, the theorem, and the conservative laws of Mei symmetry for the systems. Finally, an example is discussed for applications of the results.

Key words: regular and irregular lattice, nonholonomic system, Noether symmetry, Mei symmetry

中图分类号: (Group theory)

02.20.-a

11.30.-j (Symmetry and conservation laws) 45.05.+x (General theory of classical mechanics of discrete systems)

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.

Zhao Gang-Ling (赵纲领), Chen Li-Qun (陈立群), Fu Jing-Li (傅景礼), Hong Fang-Yu (洪方昱). Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices[J]. Chin. Phys. B, 2013, 22(3): 30201-030201.

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Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices

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