时间尺度上非完整系统Herglotz型Vacco动力学及其Noether定理
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国家自然科学基金资助项目(12272248)


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

    时间尺度定义为实数域的任意非空闭子集,统一了连续与离散系统的处理方式.文章将非完整系统的Herglotz 型Vacco动力学推广到时间尺度上,研究其Noether对称性与守恒律.首先,基于时间尺度上Herglotz变分原理,建立时间尺度上Herglotz型Vacco动力学方程.其次,根据时间尺度上的 Hamilton-Herglotz 作用量在无限小变换下的不变性,定义了时间尺度上非完整系统Herglotz型Vacco动力学的Noether对称性,给出相应的 Noether 等式.最后,证明时间尺度上非完整系统Herglotz型Vacco动力学的 Noether 定理并给出相应的守恒量.文末举例说明理论分析结果.

    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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黄智诚,张毅.时间尺度上非完整系统Herglotz型Vacco动力学及其Noether定理[J].动力学与控制学报,2026,24(2):16~25; Huang Zhicheng, Zhang Yi. Herglotz-Type Vacco Dynamics and its Noether’s Theorem for Nonholonomic Systems on Time Scales[J]. Journal of Dynamics and Control,2026,24(2):16-25.

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  • 收稿日期:2025-09-06
  • 最后修改日期:2025-10-25
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  • 在线发布日期: 2026-02-06
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