Noether symmetry and conserved quantity for a Hamilton system with time delay

doi:10.1088/1674-1056/23/5/054501

Abstract In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed, the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.

Keywords: time delay Hamilton system Noether symmetry conserved quantity

Received: 20 September 2013
Revised: 19 October 2013
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	11.30.Na	(Nonlinear and dynamical symmetries (spectrum-generating symmetries))
	02.30.Ks	(Delay and functional equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10972151 and 11272227), the Innovation Program for Scientific Research in Higher Education Institution of Jiangsu Province, China (Grant No. CXLX11_0961), and the Innovation Program for Scientific Research of Suzhou University of Science and Technology, China (Grant No. SKCX12S_039).

Corresponding Authors: Zhang Yi
E-mail: weidiezh@gmail.com

About author: 45.20.Jj; 11.30.Na; 02.30.Ks

Cite this article:

Jin Shi-Xin (金世欣), Zhang Yi (张毅) Noether symmetry and conserved quantity for a Hamilton system with time delay 2014 Chin. Phys. B 23 054501

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