Constrained Lagrangian dissipative contact dynamics

We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one constraint. As a consequence, we obtain the dynamics of contact...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-12, Vol.62 (12)
Main Authors: de León, Manuel, Laínz, Manuel, Muñoz-Lecanda, Miguel C., Román-Roy, Narciso
Format: Article
Language:English
Subjects:
Calculus of variations
Constraints
Physics
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Summary:We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one constraint. As a consequence, we obtain the dynamics of contact nonholonomic and vakonomic systems as an ordinary variational calculus with constraints on a Lagrangian with a dissipative variable. The variation of the energy and the other dissipative quantities is also obtained, giving the usual results.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0071236