EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 27 / No 3 (June 2022) Wuhan Univ. J. Nat. Sci., 27 3 (2022) 211-217 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 3, June 2022
Page(s) 211 - 217
DOI https://doi.org/10.1051/wujns/2022273211
Published online 24 August 2022
  1. Hilger S. Analysis on measure chains—A unified approach to continuous and discrete calculus [J]. Results in Mathematics, 1990, 18(1-2): 18-56. [CrossRef] [Google Scholar]
  2. Bohner M, Peterson A. Dynamic Equations on Time Scale [M]. Boston: Birkhäuser, 2001. [CrossRef] [Google Scholar]
  3. Ahlbrandt C D, Bohner M, Ridenhour J. Hamiltonian systems on time scales [J]. Journal of Mathematical Analysis and Applications, 2000, 250(2): 561-578. [CrossRef] [MathSciNet] [Google Scholar]
  4. Bohner M. Calculus of variations on time scales [J]. Dynamic Systems and Applications, 2004, 13(3-4): 339-349. [MathSciNet] [Google Scholar]
  5. Hilger S. Generalized theorem of Hartman-Grobman on measure chains [J]. Journal of the Australian Mathematical Society, 1996, 60(2): 157-191. [CrossRef] [Google Scholar]
  6. Hilger S. Differential and difference calculus-unified [J]. Nonlinear Analysis: Theory, Methods and Applications, 1997, 30(5): 2683-2694. [CrossRef] [MathSciNet] [Google Scholar]
  7. Agarwal R P, Bohner M. Basic calculus on time scales and some of its applications [J]. Results in Mathematics, 1999, 35(1-2): 3-22. [CrossRef] [Google Scholar]
  8. Bohner M, Sh Guseinov G. Double integral calculus of variations on time scales [J]. Computers and Mathematics with Applications, 2007, 54(1): 45-57. [CrossRef] [MathSciNet] [Google Scholar]
  9. Hilscher R, Zeidan V. First order conditions for generalized variational problems over time scales [J]. Computers and Mathematics with Applications, 2011, 62: 3490-3503. [CrossRef] [MathSciNet] [Google Scholar]
  10. Herzallah M A E, Muslih S I, Balwanu D, et al. Hamilton-Jacobi and fractional like action with time scaling [J]. Nonlinear Dynamics, 2011, 66(4): 549-555. [CrossRef] [MathSciNet] [Google Scholar]
  11. Han Z L, Sun S R. Vibration Theory of Dynamic Equation on Time Scale [M]. Jinan: Shandong University Press, 2014 (Ch). [Google Scholar]
  12. Fausett L V, Murty K N. Controllability, observability and realizability criteria on time scale dynamical systems [J]. Nonlinear Studies, 2004, 11(4): 627-638. [MathSciNet] [Google Scholar]
  13. Bartosiewicz Z, Kotta Ü, Pawłuszewicz E. Equivalence of linear control systems on time scales [J]. Proceedings of the Estonian Academy of Sciences Physics Mathematics, 2006, 55(1): 43-52. [CrossRef] [Google Scholar]
  14. Noether A. Invariante variations probleme. Nachrichten von der Gesellschaft der Wissenschaften zuGöttingen [J]. Mathematisch-Physikalische Klasse, 1918, 2: 235-257. [Google Scholar]
  15. Lutzky M. Dynamical symmetries and conserved quantities [J]. Journal of Physics A: Mathematical General, 1979, 12(7): 973-981. [CrossRef] [MathSciNet] [Google Scholar]
  16. Mei F X. Application of Lie Group and Lie Algebra to Constrained Mechanical Systems [M]. Beijing: Science Press, 1999 (Ch) . [Google Scholar]
  17. Mei F X. Symmetry and Conserved Quantity of Constrained Mechanical System [M]. Beijing: Beijing Institute of Technology Press, 2004 (Ch) . [Google Scholar]
  18. Zhang Y, Cai J X. Noether theorem of Herglotz-type for nonconservative Hamilton systems in event space [J]. Wuhan University Journal of Natural Sciences, 2021, 26(5): 376-382. [Google Scholar]
  19. Luo S K. Mei symmetry, Noether symmetry and Lie symmetry of Hamiltonian system [J]. Acta Physica Sinica, 2003, 52(12): 2941-2944 (Ch). [CrossRef] [MathSciNet] [Google Scholar]
  20. Chen X W, Luo S K, Mei F X. A form invariance of constrained Birkhoffian system [J]. Applied Mathematics and Mechanics, 2002, 23(1): 53-57. [CrossRef] [MathSciNet] [Google Scholar]
  21. Zhang H B, Chen H B. Noether's theorem of fractional Birkhoffian systems [J]. Journal of Mathematical Analysis and Applications, 2017, 456(2): 1442-1456. [CrossRef] [MathSciNet] [Google Scholar]
  22. Zhang Y. A set of conserved quantities from Lie symmetries for Birkhoffian systems [J]. Acta Physica Sinica, 2002, 51(3): 461-464 (Ch). [CrossRef] [MathSciNet] [Google Scholar]
  23. Bartosiewicz Z, Torres D F M. Noether's theorem on time scales [J]. Journal of Mathematical Analysis and Applications, 2008, 342(2): 1220-1226. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. Bartosiewicz Z, Martins N, Torres D F M. The second Euler-Lagrange equation of variational calculus on time scales [J]. European Journal of Control, 2011, 17(1): 9-18. [CrossRef] [MathSciNet] [Google Scholar]
  25. Malinowska A B, Ammi M R S. Noether's theorem for control problems on time scales [J]. International Journal of Difference Equations, 2014, 9(1): 87-100. [Google Scholar]
  26. Cai P P, Fu J L, Guo Y X. Noether symmetries of the nonconservative and nonholonomic systems on time scales [J]. Science China Physics, Mechanics and Astronomy, 2013, 56(5): 1017-1028. [CrossRef] [Google Scholar]
  27. Peng K K, Luo Y. Dynamics symmetries of Hamiltonian system on time scales [J]. Journal of Mathematical Physics, 2014, 55(4): 2683-2694. [Google Scholar]
  28. Song C J, Zhang Y. Noether theorem for Birkhoffian systems on time scales [J]. Journal of Mathematical Physics, 2015, 56(10): 102701. [CrossRef] [MathSciNet] [Google Scholar]
  29. Zhang Y. Noether symmetries and conserved quantities for constrained Birkhoffian systems on time scales [J]. Journal of Dynamics and Control, 2019, 17(5): 482-486. [Google Scholar]
  30. Song C J, Zhang Y. Noether theory for Birkhoffian systems with nabla derivatives [J]. Journal of Nonlinear Sciences and Applications, 2017, 10(4): 2268-2282. [CrossRef] [Google Scholar]
  31. Zhai X H, Zhang Y. Noether theorem for non-conservative systems with time delay on time scales [J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 52: 32-43. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  32. Jin S X, Zhang Y. Methods of reduction for Lagrange systems on time scales with nabla derivatives [J]. Chinese Physics B, 2017, 26(1): 243-249. [Google Scholar]
  33. Song J, Zhang Y. Routh method of reduction for dynamical systems with nonstandard Lagrangians on time scales [J]. Indian Journal of Physics, 2020, 94(4): 501-506. [NASA ADS] [CrossRef] [Google Scholar]
  34. Shi Y F, Zhang Y. Noether theorem on time scales for Lagrangian systems in event space [J]. Wuhan University Journal of Natural Sciences, 2019, 24(4): 295-304. [CrossRef] [Google Scholar]
  35. Cai P P, Fu J L, Guo Y X. Lie symmetries and conserved quantities of the constraint mechanical systems on time scales [J]. Reports on Mathematical Physics, 2017, 79(3): 279-298. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  36. Zhang Y. Adiabatic invariants and Lie symmetries on time scales for nonholonomic systems of non-Chetaev type [J]. Acta Mechanica, 2020, 231(1): 293-303. [CrossRef] [MathSciNet] [Google Scholar]
  37. Zhai X H, Zhang Y. Lie symmetry analysis on time scales and its application on mechanical systems [J]. Journal of Vibration and Control, 2019, 25(3): 581-592. [CrossRef] [MathSciNet] [Google Scholar]
  38. Zhang Y. Lie symmetry and invariants for a generalized Birkhoffian system on time scales [J]. Chaos, Solitons and Fractals, 2019, 128: 306-312. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  39. Zhang Y, Zhai X H. Perturbation to Lie symmetry and adiabatic invariants for Birkhoffian systems on time scales [J]. Communications in Nonlinear Science and Numerical Simulation, 2019, 75: 251-261. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  40. Bourdin L. Nonshifted calculus of variations on time scales with Formula -differentiable Formula [J]. Journal of Mathematical Analysis and Applications, 2014, 411(2): 543-554. [CrossRef] [MathSciNet] [Google Scholar]
  41. Anerot B, Cresson J, Belgacem K H, et al. Noether's-type theorems on time scales [J]. Journal of Mathematical Physics, 2020, 61(11): 113502. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  42. Song C J, Cheng Y. Noether's theorems for nonshifted dynamic systems on time scales [J]. Applied Mathematics and Computation, 2020, 374: 125086. [CrossRef] [MathSciNet] [Google Scholar]
  43. Song C J. Nonshifted adiabatic invariant on time scale [J]. Wuhan University Journal of Natural Sciences, 2020, 25(4): 301-306. [Google Scholar]
  44. Chen J Y, Zhang Y. Time-scale version of generalized Birkhoffian mechanics and its symmetries and conserved quantities of Noether type [J]. Advances in Mathematical Physics, 2021, 2021: 9982975. [Google Scholar]
  45. Santilli R M. Foundations of Theoretical Mechanics Ⅱ [M]. New York: Springer-Verlag, 1983. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.