EDP Sciences logo
Submit your paper
Search
Menu
All issues Volume 30 / No 1 (February 2025) Wuhan Univ. J. Nat. Sci., 30 1 (2025) 49-56 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 30, Number 1, February 2025
Page(s) 49 - 56
DOI https://doi.org/10.1051/wujns/2025301049
Published online 12 March 2025
  1. Mei F X. Advances in the symmetries and conserved quantities of classical constrained systems[J]. Advances in Mechanics, 2009, 39(1): 37-43(Ch). [Google Scholar]
  2. Mei F X. Analytical Mechanics Ⅱ[M]. Beijing: Beijing Institute of Technology Press, 2013(Ch). [Google Scholar]
  3. Chen J Y, Zhang Y. Lie symmetry theorem for nonshifted Birkhoffian systems on time scales[J]. Wuhan University Journal of Natural Sciences, 2022, 27(3): 211-217. [CrossRef] [EDP Sciences] [Google Scholar]
  4. Zhang Y. A study on time scale non-shifted Hamiltonian dynamics and Noether's theorems[J]. Wuhan University Journal of Natural Sciences, 2023, 28(2): 106-116. [CrossRef] [EDP Sciences] [Google Scholar]
  5. Djukic D S, Sutela T. Integrating factors and conservation laws for nonconservative dynamical systems[J]. International Journal of Non Linear Mechanics, 1984, 19(4): 331-339. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. Qiao Y F, Zhang Y L, Zhao S H. Integrating factors and conservation laws for the Raitzin's canonical equations of motion of nonconservative dynamical systems[J]. Acta Physica Sinica, 2002, 51(8): 1661-1665(Ch). [CrossRef] [MathSciNet] [Google Scholar]
  7. Qiao Y F, Zhang Y L, Han G C. Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics[J]. Chinese Physics, 2002, 11(10): 988-992. [Google Scholar]
  8. Qiao Y F, Zhao S H, Li R J. Integrating factors and conservation theorems of nonholonomic dynamical system of relative motion[J]. Communications in Theoretical Physics, 2007, 47(2): 217-220. [NASA ADS] [CrossRef] [Google Scholar]
  9. Zhang Y. A study of conservation laws for Chaplygin nonholonomic systems by means of integrating factors method[J]. Journal of Dynamics and Control, 2019, 17(1): 15-20(Ch). [Google Scholar]
  10. Zhang Y, Ge W K. Integrating factors and conservation laws for non-holonomic dynamical systems[J]. Acta Physica Sinica, 2003, 52(10): 2363-2367(Ch). [CrossRef] [MathSciNet] [Google Scholar]
  11. Zhou J R, Fu J L. The integrating factor and conservation quantity for constrained Hamilton system[J]. Chinese Quarterly of Mechanics, 2018, 39(3): 554-561(Ch). [Google Scholar]
  12. Santilli R M. Foundations of Theoretical Mechanics II[M]. Berlin, Heidelberg: Springer-Verlag, 1983. [CrossRef] [Google Scholar]
  13. Mei F X, Shi R C, Zhang Y F, et. al. Dynamics of Birkhoffian System[M]. Beijing: Beijing Institute of Technology Press, 1996(Ch). [Google Scholar]
  14. Zhang Y, Xue Y. Integrating factors and conservation theorems for Birkhoffian systems[J]. Chinese Quarterly of Mechanics, 2003, 24(2): 280-285(Ch). [Google Scholar]
  15. Yi Z. A general approach to the construction of conservation laws for Birkhoffian systems in event space[J]. Communications in Theoretical Physics, 2008, 50(4): 851-854. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  16. Qiao Y F, Zhao S H, Li R J. Integrating factors and conservation theorems of constrained Birkhoffian systems[J]. Chinese Physics, 2006, 15(12): 2777-2781. [NASA ADS] [CrossRef] [Google Scholar]
  17. Yang L X, Zhang Y. Integrating factors and conserved quantities for fractional Birkhoffian system[J]. Journal of Central China Normal University (Natural Sciences), 2020, 54(1): 30-35(Ch). [MathSciNet] [Google Scholar]
  18. Guenther R B, Guenther C M, Gottsch J A. The Herglotz Lectures on Contact Transformations and Hamiltonian Systems[M]. Nicolaus: Copernicus University Press, 1996. [Google Scholar]
  19. Georgieva B, Guenther R B. First Noether-type theorem for the generalized variational principle of Herglotz[J]. Topological Methods in Nonlinear Analysis, 2002, 20(2): 261-273. [CrossRef] [MathSciNet] [Google Scholar]
  20. Tian X, Zhang Y. Generalized variational principle of Herglotz type for non-conservative Lagrangian systems and its Noether's theory[J]. Journal of Nanjing University of Science and Technology, 2019, 43(6): 765-770(Ch). [MathSciNet] [Google Scholar]
  21. Cai J X, Zhang Y. Nother's theorem for Herglotz-type nonconservative Lagrange systems in event space[J]. Chinese Quarterly of Mechanics, 2022, 43(1): 122-131(Ch). [Google Scholar]
  22. Cai M Y, Zhang Y. Herglotz type Lagrange equations and Noether symmetry and conserved quantity for mechanical systems with variable mass[J]. Journal of Dynamics and Control, 2022, 20(6): 107-113(Ch). [Google Scholar]
  23. Zhang Y. Generalized variational principle of Herglotz type for nonconservative system in phase space and Noether's theorem[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(6): 1382-1389(Ch). [Google Scholar]
  24. 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]
  25. Zhang Y, Tian X. Conservation laws of nonconservative nonholonomic system based on Herglotz variational problem[J]. Physics Letters A, 2019, 383(8): 691-696. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. Dong X C, Zhang Y. Herglotz-type principle and first integrals for nonholonomic systems in phase space[J]. Acta Mechanica, 2023, 234(12): 6083-6095. [CrossRef] [MathSciNet] [Google Scholar]
  27. Dong X C, Zhang Y. Herglotz type conservation laws for nonconservative nonholonomic systems[J]. AIP Advances, 2023, 13(10): 105014. [CrossRef] [Google Scholar]
  28. Zhang Y. Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems[J]. Acta Mechanica, 2017, 228(4): 1481-1492. [CrossRef] [MathSciNet] [Google Scholar]
  29. Zhang Y, Tian X. Conservation laws for Birkhoffian systems of Herglotz type[J]. Chinese Physics B, 2018, 27(9): 090502. [NASA ADS] [CrossRef] [Google Scholar]
  30. Santos S P S, Martins N, Torres D F M. Variational problems of Herglotz type with time delay: DuBois: Reymond condition and Noether's first theorem[J]. Discrete & Continuous Dynamical Systems-A, 2015, 35(9): 4593-4610. [CrossRef] [MathSciNet] [Google Scholar]
  31. Santos S P S, Martins N, Torres D F M. Noether currents for higher-order variational problems of Herglotz type with time delay[J]. Discrete and Continuous Dynamical Systems-Series S, 2018, 11(1): 91-102. [CrossRef] [MathSciNet] [Google Scholar]
  32. Zhang Y. Noether's theorem for a time-delayed Birkhoffian system of Herglotz type[J]. International Journal of Non Linear Mechanics, 2018, 101: 36-43. [NASA ADS] [CrossRef] [Google Scholar]
  33. Zhang Y. Herglotz's variational problem for non-conservative system with delayed arguments under Lagrangian framework and its Noether's theorem[J]. Symmetry, 2020, 12(5): 845. [NASA ADS] [CrossRef] [Google Scholar]
  34. Almeida R, Malinowska A B. Fractional variational principle of Herglotz[J]. Discrete & Continuous Dynamical Systems-B, 2014, 19(8): 2367-2381. [CrossRef] [MathSciNet] [Google Scholar]
  35. Atanacković T M, Janev M, Pilipović S. Noether's theorem for variational problems of Herglotz type with real and complex order fractional derivatives[J]. Acta Mechanica, 2021, 232(3): 1131-1146. [CrossRef] [MathSciNet] [Google Scholar]
  36. Xu X X, Zhang Y. A new type of adiabatic invariant for fractional order non-conservative Lagrangian systems[J]. Acta Physica Sinica, 2020, 69(22): 220401. [CrossRef] [Google Scholar]
  37. Tian X, Zhang Y. Noether's theorem for fractional Herglotz variational principle in phase space[J]. Chaos, Solitons & Fractals, 2019, 119: 50-54. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  38. Ding J J, Zhang Y. Noether's theorem for fractional Birkhoffian system of Herglotz type with time delay[J]. Chaos, Solitons & Fractals, 2020, 138: 109913. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  39. Tian X, Zhang Y. Variational principle of Herglotz type and its Noether's theorem on time scales[J]. Chinese Quarterly of Mechanics, 2018, 39(2): 237-248(Ch). [Google Scholar]
  40. Tian X, Zhang Y. Noether symmetry and conserved quantity for Hamiltonian system of Herglotz type on time scales[J]. Acta Mechanica, 2018, 229(9): 3601-3611. [CrossRef] [MathSciNet] [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.