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Perturbation to Noether Symmetry and Noether Adiabatic Invariants of General Discrete Holonomic Systems |
| ZHANG Ming-Jiang, FANG Jian-Hui, LU Kai, ZHANG Ke-Jun |
| College of Physics Science and Technology, China University of Petroleum, Dongying 257061 |
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ZHANG Ming-Jiang, FANG Jian-Hui, LU Kai et al 2009 Chin. Phys. Lett. 26 120201 |
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Abstract The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied. First, the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given. Secondly, the concept of discrete high-order adiabatic invariant is presented, the criterion of the perturbation to Noether symmetry is established, and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained. Lastly, an example is discussed to illustrate the application of the results.
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| Keywords:
02.20.Sv
02.20.Qs
45.20.Jj
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Received: 06 July 2009
Published: 27 November 2009
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| PACS: |
02.20.Sv
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(Lie algebras of Lie groups)
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02.20.Qs
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(General properties, structure, and representation of Lie groups)
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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[1] Noether A E 1918 Nachr. Akad. Wiss.G\"{ottingenMath. Phys. 2 235
[2] Mei F X 2004 Symmetries and Conserved Quantities ofConstrained Mechanical Systems (Beijing: Beijing Institute ofTechnology Press) (in Chinese)
[3] Luo S K, Zhang Y F and et al 2008 Advances in theStudy of Dynamics of Constrained Mechanics Systems (Beijing:Science Press) (in Chinese)
[4] Levi D and Yamilov R 1997 J. Math. Phys. 386648
[5] Levi D, Tremblay S and Winternitz P 2000 J. Phys. A:Math. Gen. 33 8507
[6] Levi D, Tremblay S and Winternitz P 2001 J. Phys. A:Math. Gen. 34 9507
[7] Dorodnitsyn V 2001 Appl. Numer. Math. 39 307
[8] Shi S Y, Fu J L and Chen L Q 2008 Chin. Phys. B 17 385
[9] Shi S Y, Chen L Q and Fu J L 2008 Commun. Theor.Phys. 50 607
[10] Fu J L, Chen B Y and Xie F P 2008 Chin. Phys. B 17 4354
[11] Burgers J M 1917 Ann. Physik. 357 195
[12] Zhao Y Y and Mei F X 1999 Symmetries and Invariantsof Mechanical Systems (Beijing: Science Press) p164 (in Chinese)
[13] Chen X W and Mei F X 2000 Chin. Phys. 9 721
[14] Zhang Y 2002 Acta Phys. Sin. 51 2417 (inChinese)
[15] Chen X W, Li Y M and Zhao Y H 2005 Phys. Lett. A 337 274
[16] Zhang Y 2006 Chin. Phys. 15 1935
[17] Luo S K, Chen X W and Guo Y X 2007 Chin. Phys. 16 3176
[18] Ding N, Fang J H, Wang P and Zhang X N 2007 Commun.Theor. Phys. 48 19
[19] Luo S K 2007 Chin. Phys. Lett. 24 2463
[20] Zhang M J, Fang J H, Zhang X N and Lu K 2008 Chin.Phys. B 17 1957
[21] Wang P, Fang J H and Wang X M 2009 Chin. Phys.Lett. 26 034501
[22] Pang T, Fang J H, Zhang M J, Lin P and Lu K 2009 Chin. Phys. Lett. 26 070203 |
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