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Approximate Noether theorem and its inverse for nonlinear dynamical systems with approximate nonstandard Lagrangian

Author

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  • Jin, Shi-Xin
  • Chen, Xiang-Wei
  • Li, Yan-Min

Abstract

The approximate Noether theorem and its inverse theorem for the nonlinear dynamical systems with approximate exponential Lagrangian and approximate power-law Lagrangian are investigated. For each case, the approximate differential equations of motion for the nonlinear dynamical systems with approximate nonstandard Lagrangian are established, the generalized Noether identities are given. The relationship between the approximate Noether symmetries and approximate conserved quantities for the system with approximate nonstandard Lagrangian are established, and the approximate Noether theorems and their inverse theorems are obtained. Two examples are given to illustrate the application of the results.

Suggested Citation

  • Jin, Shi-Xin & Chen, Xiang-Wei & Li, Yan-Min, 2024. "Approximate Noether theorem and its inverse for nonlinear dynamical systems with approximate nonstandard Lagrangian," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003424
    DOI: 10.1016/j.chaos.2024.114790
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    References listed on IDEAS

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    1. Ding, Juan-Juan & Zhang, Yi, 2020. "Noether’s theorem for fractional Birkhoffian system of Herglotz type with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.
    3. Matteo Gorgone & Francesco Oliveri, 2021. "Approximate Noether Symmetries of Perturbed Lagrangians and Approximate Conservation Laws," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    4. Zhang, Yi & Jia, Yun-Die, 2023. "Generalization of Mei symmetry approach to fractional Birkhoffian mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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