Chin. Phys. B, 2013, Vol. 22(3): 030201    DOI: 10.1088/1674-1056/22/3/030201
 GENERAL Next

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

Zhao Gang-Linga b d, Chen Li-Quna b, Fu Jing-Lic, Hong Fang-Yuc
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
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.
Received:  17 June 2012      Published:  01 February 2013
 PACS: 02.20.-a (Group theory) 02.30.lk 11.30.-j (Symmetry and conservation laws) 45.05.+x (General theory of classical mechanics of discrete systems)
Fund: 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).
Corresponding Authors:  Fu Jing-Li     E-mail:  sqfujingli@163.com