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Chin. Phys. B, 2014, Vol. 23(5): 054501    DOI: 10.1088/1674-1056/23/5/054501

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

Jin Shi-Xina, Zhang Yib
a College of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China;
b College of Civil Engineering, Suzhou University of Science and Technology, Suzhou 215011, China
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      Published:  15 May 2014
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:
About author:  45.20.Jj; 11.30.Na; 02.30.Ks

Cite this article: 

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

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