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Lie symmetries and conserved quantities of discrete constrained Hamilton systems

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Języki publikacji
EN
Abstrakty
EN
In this paper, the Lie symmetry theory of discrete singular systems is studied in phase space. Firstly, the discrete canonical equations and the energy evolution equations of the constrained Hamilton systems are established based on the discrete difference variational principle. Secondly, the Lie point transformation of discrete group is applied to the difference equations and constraint restriction, and the Lie symmetry determination equations of the discrete constrained Hamilton systems are obtained; Meanwhile, the Lie symmetries of singular systems lead to the discrete Noehter type conserved quantities when the structure condition equations (discrete Noether identity) are established. Finally,an example is given to illustrate the application, the results show that the conservative constrained Hamilton systems also have the discrete energy conservation.
Rocznik
Strony
61--70
Opis fizyczny
Bibliogr 21 poz.
Twórcy
autor
  • School of Electrical and Mechanical Engineering, Taihu University of Wuxi Wuxi, China
Bibliografia
  • [1] Dirac, P.A.M. (1964). Lecture on Quantum Mechanics. NewYork: Yeshi-va University Press.
  • [2] Mei, F.X. (1999). The application of Liegroup and Lie algebra to the constrained mechanical systems. Beijing: Science Press (in Chinese).
  • [3] Noether, E. (1918). Invariante variationsprobleme. Nachr. König. Gesell. Wissen. Göttingen, Math. Phys. KI., 2, 235-257.
  • [4] Lutzky, M. (1995). Remarks on a recent theorem about conserved quantities. J. Phys. A: Math. Gen., 28(11), 637-638.
  • [5] Mei, F.X. (2000). Form invariance of Lagrange system. Beijing Institute of Technology, 9(2), 120-124.
  • [6] Li, Z.P. (1992). The regular form’s generalized Noether theorem of nonholonomic singular systems and its inverse theorem. Huang Huai Journal, 3(1), 8-16 (in Chinese).
  • [7] Zhang, Y., & Xue, Y. (2001). Lie symmetries of constraint Hamiltonian system with the second type of constraints. Acta Phys. Sinica, 50(5), 816-819 (in Chinese).
  • [8] Luo, S.K. (2004). Mei symmetries, Noether symmetries and Lie symmetries of Hamiltonian canonical equations of singular systems. Acta Phys. Sinica, 53(1), 5-11 (in Chinese).
  • [9] Li, Y.C., Zhang, Y., & Liang, J.H. (2002). Lie symmetries and conservation of a class of nonholonomic singular systems. Acta Phys. Sinica, 51(10), 2186-2190 (in Chinese).
  • [10] Zheng, M.L. (2017). Perturbation and adiabatic invariants constrained Hamilton of Mei symmetry for system. Journal of Yanbian University (Natural Scicnce), 43(4), 328-335 (in Chinese).
  • [11] Cadzow, J.A. (1970). Discrete calculus of variations. International Journal of Control, 11(3), 393-407.
  • [12] Lee, T. (1983). Can time be a discrete dynamical variable. Phys. Lett. B, 122(3), 217-220.
  • [13] Guo, H.Y., Li, Y.Q, Wu, K., et al. (2002). Difference discrete variational principles, Euler-Lagrange cohomology and sympletic, multisympletic structures I: difference discretevariational principle. Communications in Theoretical Physics, 37(1), 1-10.
  • [14] Fu, J.L., Dai, G.D., Salvador, J., & Tang Y.F. (2007). Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems. Chin. Phys., 16(3), 570-577.
  • [15] Fu, J.L., Chen, B.Y., & Chen, L.Q. (2009). Noether symmetries of discrete nonholonomic dynamical systems. Phys. Lett. A, 373(4), 409-412.
  • [16] Shi, S.Y., Fu, J.L., & Chen, L.Q. (2008). The Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. Chin. Phys. B, 17(2), 385-389.
  • [17] Dorodnitsyn, V. (1994). Finite difference models entirely inheriting continuous symmetry of original differential equations. Int. J. Mod. Phys. C, 5(04), 723-734.
  • [18] Lu, K., Fang, J.H., Zhang, M.J., et al. (2009). Noether symmetries and Mei symmetries of discrete holonomic systems in phase space. Acta Phys. Sinica, 58(11), 7421-7426 (in Chinese).
  • [19] Xu, R.L. (2014). Study on MNL symmetries and new conservation of discrete mechanical systems. Shandong: China University of Petroleum (in Chinese).
  • [20] Xia, L.L., & Chen L.Q. (2012). Mei symmetries and conserved quantities for non-conservative Hamiltonian difference systems with irregular lattices. Nonlinear Dynamics, 70(2), 1223-1230.
  • [21] Li, Z.P. (1999). Constrained Hamiltonian system and its symmetric properties. Beijing: Beijing University of Technology Press (in Chinese).
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-f63c57cd-6340-4fb4-aa83-2ff0345d2eff
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