HerglotzType Vacco Dynamics and its Noether’s Theorem for Nonholonomic Systems on Time Scales
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    Abstract:

    Time scales are defined as any nonempty closed subset of the real number field, which unifies the treatment of continuous and discrete systems. In this paper, the Herglotztype Vacco dynamics of nonholonomic systems are extended to the time scales, and its Noether symmetry and conservation law are investigated. Firstly, based on the Herglotz variational principle on time scales, the Herglotztype Vacco dynamics equations on time scales are established. Secondly, according to the invariance of HamiltonHerglotz action on time scales under infinitesimal transformations, the Noether symmetry of Herglotztype Vacco dynamics of nonholonomic systems on time scales is defined, and the corresponding Noether identities are presented. Finally, the Noether’s theorem of Herglotztype Vacco dynamics for nonholonomic systems on time scales is proven, and the corresponding conserved quantities are provided. At the conclusion of the paper, two examples are presented to demonstrate the results of theoretical analysis.

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History
  • Received:September 06,2025
  • Revised:October 25,2025
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  • Online: February 06,2026
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