Herglotz-type principle and first integrals for nonholonomic systems in phase space

Dong, Xin-Chang; Zhang, Yi

doi:10.1007/s00707-023-03707-y

Cited by 2 publications

(1 citation statement)

References 33 publications

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“…Almeida et al [23] proposed the fractional Herglotz principle by extending the Herglotz principle to fractional models. Zhang et al [24][25][26] extended the Herglotz principle and its Noether theorems to Birkhoffian systems, nonconservative nonholonomic systems, etc. However, as far as we know, no research has been conducted on the Herglotz principle and its conserved quantities for nonholonomic systems based on fractional models.…”

Section: Introductionmentioning

confidence: 99%

Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints

Deng,

Zhang

2024

Fractal Fract

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This research aims to investigate the Noether symmetry and conserved quantity for the fractional Lagrange system with nonholonomic constraints, which are based on the Herglotz principle. Firstly, the fractional-order Herglotz principle is given, and the Herglotz-type fractional-order differential equations of motion for the fractional Lagrange system with nonholonomic constraints are derived. Secondly, by introducing infinitesimal generating functions of space and time, the Noether symmetry of the Herglotz type is defined, along with its criteria, and the conserved quantity of the Herglotz type is given. Finally, to demonstrate how to use this method, two examples are provided.

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Section: Introductionmentioning

confidence: 99%

Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints

Deng,

Zhang

2024

Fractal Fract

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Herglotz-type vakonomic dynamics and its Noether symmetry for nonholonomic constrained systems

Huang,

Zhang

2024

Journal of Mathematical Physics

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In this paper, Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems are studied. Firstly, Herglotz-type vakonomic dynamical equations for nonholonomic systems are derived on the premise of Herglotz variational principle. Secondly, in terms of the Herglotz-type vakonomic dynamical equations, the Noether symmetry of Herglotz-type vakonomic dynamics is explored, and the Herglotz-type vakonomic dynamical Noether theorems and their inverse theorems are deduced. Finally, the conservation laws of Appell–Hamel case with non-conservative forces are analyzed to show the validity of our results.

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Herglotz-type principle and first integrals for nonholonomic systems in phase space

Cited by 2 publications

References 33 publications

Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints

Noether’s Theorem of Herglotz Type for Fractional Lagrange System with Nonholonomic Constraints

Herglotz-type vakonomic dynamics and its Noether symmetry for nonholonomic constrained systems

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