Noether's theory of Lagrange systems in discrete case

doi:10.1088/1674-1056/20/1/011101

Abstract In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.

Keywords: discrete Lagrange system difference functional Noether-type identity Noether-type theorem

Received: 28 February 2010
Revised: 01 July 2010
Accepted manuscript online:

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

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10872037) and the Natural Science Foundation of Anhui Province, China (Grant No. 070416226).

Cite this article:

Lü Hong-Sheng(吕洪升), Zhang Hong-Bin(张宏彬), and Gu Shu-Long(顾书龙) Noether's theory of Lagrange systems in discrete case 2011 Chin. Phys. B 20 011101

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