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All issues Volume 29 / No 2 (April 2024) Wuhan Univ. J. Nat. Sci., 29 2 (2024) 106-116 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 29, Number 2, April 2024
Page(s) 106 - 116
DOI https://doi.org/10.1051/wujns/2024292106
Published online 14 May 2024
  1. Arnold V I. Mathematical Methods of Classical Mechanics [M]. New York: Springer-Verlag, 1978. [Google Scholar]
  2. El-Nabulsi R A. Nonlinear dynamics with non-standard Lagrangians [J]. Qualitative Theory of Dynamical Systems, 2013, 12(2): 273-291. [Google Scholar]
  3. Saha A, Talukdar B. Inverse variational problem for nonstandard Lagrangians [J]. Reports on Mathematical Physics, 2014, 73(3): 299-309. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  4. Saha A, Talukdar B. On the non-standard Lagrangian equations [EB/OL]. [2013-01-12]. https://arxiv.org/ftp/arxiv/papers/1301/1301.2667.pdf. [Google Scholar]
  5. Muslelak Z E. Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients [J]. Journal of Physics A: Mathematical and Theoretical, 2008, 41(5): 055205. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. 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]
  7. Chen J Y, Zhang Y. Lie symmetry theorem for non-shifted Birkhoffian systems on time scales [J]. Wuhan University Journal of Natural Sciences, 2022, 27(3): 211-217. [CrossRef] [EDP Sciences] [Google Scholar]
  8. 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]
  9. Zhang Y, Zhou X S. Noether theorem and its inverse for nonlinear dynamical systems with nonstandard Lagrangians [J]. Nonlinear Dynamics, 2016, 84(4): 1867-1876. [CrossRef] [MathSciNet] [Google Scholar]
  10. Song J, Zhang Y. Noether symmetry and conserved quantity for dynamical system with non-standard Lagrangians on time scales [J]. Chinese Physics B, 2017, 26(8): 084501. [NASA ADS] [CrossRef] [Google Scholar]
  11. Song J, Zhang Y. Noether's theorems for dynamical systems of two kinds of non-standard Hamiltonians [J]. Acta Mechanica, 2018, 229(1): 285-297. [CrossRef] [MathSciNet] [Google Scholar]
  12. Zhang L J, Zhang Y. Non-standard Birkhoffian dynamics and its Noether's theorems [J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 91: 105435. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  13. Zhang Y, Wang X P. Lie symmetry perturbation and adiabatic invariants for dynamical system with non-standard Lagrangians [J]. International Journal of Non-Linear Mechanics, 2018, 105: 165-172. [NASA ADS] [CrossRef] [Google Scholar]
  14. Jia Y D, Zhang Y. Fractional Birkhoffian dynamics based on quasi⁃fractional dynamics models and its Lie symmetry [J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2021, 38(1): 84-95. [Google Scholar]
  15. Zhang Y, Wang X P. Mei symmetry and invariants of quasi-fractional dynamical systems with non-standard Lagrangians [J]. Symmetry, 2019, 11 (8):1061. [CrossRef] [Google Scholar]
  16. Zhou X S, Zhang Y. Generalized energy integral and Whittaker method of reduction for dynamics systems with Non-standard Lagrangians [J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2017, 49(2): 269-275(Ch). [Google Scholar]
  17. Zhou X S, Zhang Y. Routh method of reduction for dynamic systems with non-standard Lagrangians [J]. Chinese Quarterly of Mechanics, 2016, 37(1): 5-21(Ch). [Google Scholar]
  18. Cieśliński J I, Nikiciuk T A. Direct approach to the construction of standard and non-standard Lagrangians for dissipative-like dynamical systems with variable coefficients [J]. Journal of Physics A: Mathematical and Theoretical, 2010, 43(17): 175205. [CrossRef] [MathSciNet] [Google Scholar]
  19. Bagchi B, Ghosh D, Modak S, et al. Nonstandard Lagrangians and branching: The case of some nonlinear Liénard systems [J]. Modern Physics Letters A, 2019, 34(14): 1950110. [CrossRef] [MathSciNet] [Google Scholar]
  20. Liu S X, Guan F, Wang Y. The nonlinear dynamics based on the non-standard Hamiltonians [J]. Nonlinear Dynamics, 2017, 88(2):1229-1236. [CrossRef] [MathSciNet] [Google Scholar]
  21. Chandrasekar V K, Senthilvelan M, Lakshmanan M. Unusual Liénard-type nonlinear oscillator [J]. Physics Review E, 2005, 72(6): 066203. [Google Scholar]
  22. Chandrasekar V K, Senthilvelan M, Lakshmanan M. On the Lagrangian and Hamiltonian description of the damped linear harmonic oscillator [J]. Journal of Mathematical Physics, 2007, 48(3): 032701. [CrossRef] [MathSciNet] [Google Scholar]
  23. Muslelak Z E, Roy D, Swift L D. Method to drive Lagrangian and Hamiltonian for a nonlinear dynamical system with variable coefficients [J]. Chaos, Solitons & Fractals, 2008, 38(3): 894-902. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  24. EI-Nabulsi R A. Non-standard fractional Lagrangians [J]. Nonlinear Dynamics, 2013, 74(1): 381-394. [CrossRef] [MathSciNet] [Google Scholar]
  25. EI-Nabulsi R A. Non-standard power-law Lagrangians in classical and quantum dynamics [J]. Applied Mathematics Letters, 2015, 43: 120-127. [CrossRef] [MathSciNet] [Google Scholar]
  26. EI-Nabulsi R A. Gravitational field as a pressure force from logarithmic Lagrangians and non-standard Hamiltonians: The case of stellar halo of Milky Way [J]. Communications in Theoretical Physics, 2018, 69(3): 233-240. [CrossRef] [MathSciNet] [Google Scholar]
  27. Chen B. Analytical Dynamics[M]. 2nd Ed. Beijing: Peking University Press, 2012(Ch). [Google Scholar]
  28. Mei F X, Wu H B, Li Y M. A Brief History of Analytical Mechanics [M]. Beijing: Science Press, 2019(Ch). [Google Scholar]
  29. Mei F X. Canonical transformation for weak nonholonomic systems [J]. Chinese Science Bulletin, 1993, 38(4): 281-285. [Google Scholar]
  30. Zhang Y. Theory of canonical transformation for a fractional mechanical system [J]. Acta Mathematicae Applicatae Sinica, 2016, 39(2): 249-260(Ch). [MathSciNet] [Google Scholar]
  31. Zhang Y. The generalized canonical transformations of Birkhoffian systems and their basic formulations [J]. Chinese Quarterly of Mechanics, 2019, 40(4): 656-665(Ch). [Google Scholar]
  32. Zhang Y. Theory of generalized canonical transformations for Birkhoff systems [J]. Advances in Mathematical Physics, 2020, 2020: 9482356. [Google Scholar]
  33. Zhang Y, Zhai X H. Generalized canonical transformation for second order Birkhoffian systems on time scales[J]. Theoretical and Applied Mechanics Letters, 2019, 9(6): 353-357. [CrossRef] [Google Scholar]
  34. Mei F X. Applications of Lie Groups and Lie Algebras to Constrained Mechanical Systems [M]. Beijing: Science Press, 1999 (Ch). [Google Scholar]
  35. Zhang Y, Mei F X. Algebraic structure of the dynamical equations of holonomic mechanical system in relative motion [J]. Journal of Beijing Institute of Technology, 1998, 7(1): 12-18. [Google Scholar]
  36. Mei F X, Shi R C, Zhang Y F. Poisson's theory of the Chaplygin's equations [J]. Journal of Beijing Institute of Technology, 1995, 4(2): 123-129. [Google Scholar]
  37. Zhang Y, Shang M. Poisson theory and integration method for a dynamical system of relative motion [J]. Chinese Physics B, 2011, 20(2): 024501. [NASA ADS] [CrossRef] [Google Scholar]
  38. Fu J L, Chen X W, Luo S K. Algebraic structures and Poisson integrals of relativistic dynamical equations for rotational systems [J]. Applied Mathematics and Mechanics, 1999, 10(11): 1266-1274. [Google Scholar]
  39. Mei F X. Poission's theory of Birkhoffian system [J]. Chinese Science Bulletin, 1996, 41(8): 641. [MathSciNet] [Google Scholar]
  40. Luo S K, Chen X W, Guo Y X. Algebraic structure and Poisson integrals of rotational relativistic Birkhoff system [J]. Chinese Physics, 2002, 11(6): 523-528. [NASA ADS] [CrossRef] [Google Scholar]
  41. Zhang Y. Poisson theory and integration method of Birkhoffian systems in the event space [J]. Chinese Physics B, 2010, 19(8): 080301. [NASA ADS] [CrossRef] [Google Scholar]

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