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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 |
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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.
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Received: 20 September 2013
Revised: 19 October 2013
Accepted manuscript online:
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PACS:
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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11.30.Na
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(Nonlinear and dynamical symmetries (spectrum-generating symmetries))
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02.30.Ks
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(Delay and functional equations)
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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
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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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[1] |
Hu H Y and Wang Z H 1999 Adv. Mech. 29 501 (in Chinese)
|
[2] |
Xu J and Pei L J 2006 Adv. Mech. 36 17 (in Chinese)
|
[3] |
Wang Z H and Hu H Y 2013 Adv. Mech. 43 3 (in Chinese)
|
[4] |
El'sgol'c L E, Brown A A and Danskin J M 1964 Qualitative Methods of Mathematical Analysis (Providence: American Mathematical Society)
|
[5] |
Hughes D K 1968 J. Optim. Theory Appl. 2 1
|
[6] |
Palm W J and Schmitendorf W E 1974 J. Optim. Theory Appl. 14 599
|
[7] |
Rosenblueth J F 1988 IMA J. Math. Control Inform. 5 125
|
[8] |
Rosenblueth J F 1988 IMA J. Math. Control. Inform. 5 285
|
[9] |
Chan W L and Yung S P 1993 J. Optim. Theory Appl. 76 131
|
[10] |
Lee C H and Yung S P 1996 J. Optim. Theory. Appl. 88 157
|
[11] |
Frederico G S F and Torres D F M 2012 Numer. Algebra Control Optim. 2 619
|
[12] |
Djukic Dj S and Vujanovic B 1975 Acta Mech. 23 17
|
[13] |
Li Z P 1981 Acta Phys. Sin. 30 1699 (in Chinese)
|
[14] |
Bahar L Y and Kwatny H G 1987 Int. J. Non-Linear Mech. 22 125
|
[15] |
Liu D 1991 Sci. China Ser. A 34 419
|
[16] |
Luo S K 1991 Appl. Math. Mech. 12 927
|
[17] |
Mei F X 1993 Sci. China Ser. A 36 1456
|
[18] |
Zhang Y, Shang M and Mei F X 2000 Chin. Phys. 9 401
|
[19] |
Fu J L, Chen B Y and Chen L Q 2009 Phys. Lett. A 373 409
|
[20] |
Bluman G W and Anco S C 2002 Symmety and Integration Methods for Differential Equations (New York: Springer-Verlag)
|
[21] |
Lutzky M 1979 J. Phys. A: Math. Gen. 12 973
|
[22] |
Hojman S A 1992 J. Phys. A: Math. Gen. 25 L291
|
[23] |
Zhao Y Y 1994 Acta Mech. Sin. 26 380 (in Chinese)
|
[24] |
Mei F X 1999 Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems (Beijing: Science Press) (in Chinese)
|
[25] |
Zhang Y 2002 Acta Phys. Sin. 51 461 (in Chinese)
|
[26] |
Luo S K, Cai J L and Jia L Q 2005 Commun. Theor. Phys. 43 193
|
[27] |
Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese)
|
[28] |
Hojman S 1984 J. Phys. A: Math. Gen. 17 2399
|
[29] |
Mei F X and Wu H B 2008 Phys. Lett. A 372 2141
|
[30] |
Zhang Y 2011 Chin. Phys. B 20 034502
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