PL EN


Preferences help
enabled [disable] Abstract
Number of results
2011 | 119 | 3 | 298-303
Article title

Perturbation to Symmetry and Adiabatic Invariants of General Discrete Holonomic Dynamical Systems

Authors
Content
Title variants
Languages of publication
EN
Abstracts
EN
This paper investigates perturbation to the Noether symmetry of discrete holonomic nonconservative dynamical systems on a uniform lattice. Firstly, we give the Noether theorem of system. Secondly, both criterion of perturbation to the Noether symmetry and the Noether adiabatic invariants of system are obtained. Finally, an example is given to illustrate these results.
Keywords
EN
Contributors
author
  • College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi, Xinjiang 830054, China
author
  • College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi, Xinjiang 830054, China
References
  • 1. E. Noether, Kgl. Ges. Wiss. Nachr. Göttingen Math. Phys. 2, 235 (1918)
  • 2. D.S. Djukić, B.D. Vujanović, Acta Mech. 23, 17 (1975)
  • 3. W. Sarlet, F. Cantrijn, SIAM Rev. 23, 467 (1981)
  • 4. L.Y. Bahar, H.G. Kwatny, Int. J. Non-Linear Mech. 22, 125 (1987)
  • 5. M. Lutzky, J. Phys. A, Math. Gen. 12, 973 (1979)
  • 6. G.E. Prince, C.J. Eliezer, J. Phys. A, Math. Gen. 14, 587 (1981)
  • 7. F.X. Mei, Symmetries and Conserved Quantities of Constrained Mechanical Systems, Institute of Technology Press, Beijing 2004 (in Chinese)
  • 8. S.A. Hojman, J. Phys. A, Math. Gen. 25, L291 (1992)
  • 9. M. Lutzky, J. Phys. A, Math. Gen. 28, L637 (1995)
  • 10. J. Goedert, F. Haas, Phys. Lett. A 239, 348 (1998)
  • 11. Y.X. Guo, S.K. Luo, M. Shang, F.X. Mei, Rep. Math. Phys. 47, 313 (2001)
  • 12. J.L. Fu, L.Q. Chen, J. Salvador, Y.F. Tang, Phys. Lett. A 358, 5 (2006)
  • 13. Y. Zhang, Chin. Phys. B 18, 4636 (2009)
  • 14. J.H. Fang, M.J. Zhang, W.W. Zhang, Phys. Lett. A 374, 1801 (2010)
  • 15. J.L. Cai, Acta Phys. Pol. A 117, 445 (2010)
  • 16. S. Maeda, Math. Jpn. 25, 405 (1980)
  • 17. D. Levi, P. Winternitz, J. Math. Phys. 37, 5551 (1996)
  • 18. D. Levi, S. Tremblay, P. Winternitz, J. Phys. A, Math. Gen. 34, 9507 (2001)
  • 19. V.A. Dorodnitsyn, J. Sov. Math. 55, 1490 (1991)
  • 20. V.A. Dorodnitsyn, R.V. Kozlov, P. Winternitz, J. Math. Phys. 41, 480 (2000)
  • 21. V.A. Dorodnitsyn, Appl. Numer. Math. 307, 321 (2001)
  • 22. J.E. Marsden, M. West, Acta Numer. 357 (2001)
  • 23. P.E. Hydon, Proc. R. Soc. A 456, 2835 (2000)
  • 24. H.B. Zhang, L.Q. Chen, R.W. Liu, Chin. Phys. 14, 1063 (2005)
  • 25. J.L. Fu, B.Y. Chen, L.Q. Chen, Phys. Lett. A 373, 409 (2009)
  • 26. Y.Y. Zhao, F.X. Mei, Symmetries and Invariants of Mechanical Systems, Science Press, Beijing 1999 (in Chinese)
  • 27. V.A. Baikov, R.K. Gazizov, N.H. Ibragimov, J. Sov. Math. 55, 1450 (1991)
  • 28. V.A. Baikov, R.K. Gazizov, N.H. Ibragimov, in: CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 3, Ed. N.H. Ibragimov, CRC Press, Boca Raton, Florida 1996, p. 31
  • 29. A.H. Kara, F.M. Mahomed, G. Ünal, Int. J. Theor. Phys. 38, 2389 (1999)
  • 30. A.G. Johnpillai, A.H. Kara, Int. J. Theor. Phys. 40, 1501 (2001)
  • 31. J.L. Fu, L.Q. Chen, Phys. Lett. A 324, 95 (2004)
  • 32. X.W. Chen, Y.M. Li, Y.H. Zhao, Phys. Lett. A 337, 274 (2005)
  • 33. Y. Zhang, C.X. Fan, F.X. Mei, Acta Phys. Sin. 55, 3237 (2006) (in Chinese)
  • 34. S.K. Luo, Acta Phys. Sin. 57, 5580 (2007) (in Chinese)
  • 35. P. Wang, J.H. Fang, X.M. Wang, Chin. Phys. Lett. 26, 034501 (2009)
  • 36. M.J. Zhang, J.H. Fang, K. Lu, Int. J. Theor. Phys. 49, 427 (2010)
  • 37. N. Ding, X.F. Chen, J.H. Fang, C.Z. Liu, Phys. Lett. A 373, 3005 (2009)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv119n304kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.