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Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems with delayed arguments

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  • Huang, Li-Qin
  • Zhang, Yi

Abstract

The Herglotz-type vakonomic dynamics of nonholonomic constrained systems with delayed arguments and its Noether theory are studied in this paper. First of all, the Herglotz-type equations of time-delayed vakonomic dynamics for nonholonomic systems are established, and the Herglotz-type local extremal equations are given. Secondly, on the basis of derivation of the variational formulas of Hamilton–Herglotz action with time delay, the Herglotz-type Noether symmetry criteria for time-delayed vakonomic dynamics are investigated. Thirdly, the Herglotz-type Noether’s theorems and inverse theorems for time-delayed vakonomic dynamics of nonholonomic systems are deduced. Finally, an example is presented to demonstrate the application of the results.

Suggested Citation

  • Huang, Li-Qin & Zhang, Yi, 2024. "Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems with delayed arguments," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924004065
    DOI: 10.1016/j.chaos.2024.114854
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    References listed on IDEAS

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    1. Shi-Xin Jin & Yi Zhang, 2015. "Noether Theorem for Nonholonomic Systems with Time Delay," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, April.
    2. Garra, Roberto & Taverna, Giorgio S. & Torres, Delfim F.M., 2017. "Fractional Herglotz variational principles with generalized Caputo derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 94-98.
    3. 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).
    4. Tian, Xue & Zhang, Yi, 2019. "Noether’s theorem for fractional Herglotz variational principle in phase space," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 50-54.
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