Herglotz-type vakonomic dynamics and its Noether symmetry for nonholonomic constrained systems. (English) Zbl 1543.70012
Summary: 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.
©2024 American Institute of Physics
©2024 American Institute of Physics
MSC:
| 70H30 | Other variational principles in mechanics |
| 70G75 | Variational methods for problems in mechanics |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
| 49S05 | Variational principles of physics |
| 37J60 | Nonholonomic dynamical systems |
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