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

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

中国物理B ›› 2014, Vol. 23 ›› Issue (5): 54501-054501.doi: 10.1088/1674-1056/23/5/054501

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

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

金世欣^a, 张毅^b

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

收稿日期:2013-09-20 修回日期:2013-10-19 出版日期:2014-05-15 发布日期:2014-05-15
基金资助:
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).

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

Jin Shi-Xin (金世欣)^a, Zhang Yi (张毅)^b

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

Received:2013-09-20 Revised:2013-10-19 Online:2014-05-15 Published:2014-05-15
Contact: Zhang Yi E-mail:weidiezh@gmail.com
About author:45.20.Jj; 11.30.Na; 02.30.Ks
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: time delay, Hamilton system, Noether symmetry, conserved quantity

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.

Key words: time delay, Hamilton system, Noether symmetry, conserved quantity

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

11.30.Na (Nonlinear and dynamical symmetries (spectrum-generating symmetries)) 02.30.Ks (Delay and functional equations)

金世欣, 张毅. Noether symmetry and conserved quantity for a Hamilton system with time delay[J]. 中国物理B, 2014, 23(5): 54501-054501.

Jin Shi-Xin (金世欣), Zhang Yi (张毅). Noether symmetry and conserved quantity for a Hamilton system with time delay[J]. Chin. Phys. B, 2014, 23(5): 54501-054501.

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

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

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