A K-contact Lagrangian formulation for nonconservative field theories

Gaset, Jordi; Gràcia, Xavier; Muñoz-Lecanda, Miguel C.; Rivas, Xavier; Román‐Roy, Narciso

doi:10.1016/s0034-4877(21)00041-0

Cited by 27 publications

(38 citation statements)

References 18 publications

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“…Then the dynamical vector field is completely determined except for the Lagrange multipliers. The multiplier µ is obtained form equation (30). The integral curves of the vector field Y L are the dynamical trajectories of the system.…”

Section: For Dsmentioning

confidence: 99%

“…More recently, the study of the geometrization of dissipative systems [10,27,46], in its natural framework of contact geometry [3,32,39], has gained momentum, although the Lagrangian version was available since the 1930s thanks to the developments of Gustav Herglotz [37,38]. Contact mechanics [6,8,9,12,16,17,17,19,28,41] is also the natural framework for studying thermodynamics as early as Constantin Carathéodory (the first quarter of the past century), although its applications today cover many other fields [7,12,29,30,35,39,48,49].…”

Section: Introductionmentioning

confidence: 99%

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Constrained Lagrangian dissipative contact dynamics

de León,

Laínz,

Muñoz-Lecanda

et al. 2021

Preprint

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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 ordinary variational calculus with constraints on a Lagrangian with a dissipative variable. The variation of the energy and the other dissipative quantities are also obtained giving the usual results.

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Section: For Dsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constrained Lagrangian dissipative contact dynamics

de León,

Laínz,

Muñoz-Lecanda

et al. 2021

Preprint

Self Cite

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“…In a series of papers [39,40], the authors have developed a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. The geometric is the natural extension of k-symplectic structures, so instead to use k copies of the canonical symplectic structure on the cotangent bundle T M , the authors consider k copies of the natural contact structure on the extended cotangent bundle T * M × R, obtaining the notions of k-contact structure and k-contact Hamiltonian system.…”

Section: • Classical Field Theories With Dissipationmentioning

confidence: 99%

A review on contact Hamiltonian and Lagrangian systems

León¹,

Laínz²

2020

Preprint

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Contact Hamiltonian dynamics is a subject that has still a short history, but with relevant applications in many areas: thermodynamics, cosmology, control theory, and neurogeometry, among others. In recent years there has been a great effort to study this type of dynamics both in theoretical aspects and in its potential applications in geometric mechanics and mathematical physics. This paper is intended to be a review of some of the results that the authors and their collaborators have recently obtained on the subject.

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“…The notion of k-contact Hamiltonian system was introduced in [20] and was used to describe several PDE's of interest. This was later applied to Lagrangian field theory [22].…”

Section: Introductionmentioning

confidence: 99%

“…The aim of the present work is to describe the Skinner-Rusk formalism for classical field theories with dissipation. We start from the Lagrangian and Hamiltonian k-contact description for these kinds of systems introduced in [20,22], generalizing the unified formalisms previously developed for contact mechanics in [14] and for the k-symplectic formulation of classical field theories in [39].…”

Section: Introductionmentioning

confidence: 99%

Skinner-Rusk formalism for k-contact systems

Gràcia,

Rivas,

Román-Roy

2021

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In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian systems, which is based on the k-symplectic formulation of field theories as well as on contact geometry. In this work we present the Skinner-Rusk unified setting for these kinds of theories, which encompasses both the Lagrangian and Hamiltonian formalisms into a single picture. This unified framework is specially useful when dealing with singular systems, since: (i) it incorporates in a natural way the second-order condition for the solutions of field equations, (ii) it allows to implement the Lagrangian and Hamiltonian constraint algorithms in a unique simple way, and (iii) it gives the Legendre transformation, so that the Lagrangian and the Hamiltonian formalisms are obtained straightforwardly. We apply this description to several interesting physical examples: the damped vibrating string, the telegrapher's equations, and Maxwell's equations with dissipation terms.

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A K-contact Lagrangian formulation for nonconservative field theories

Cited by 27 publications

References 18 publications

Constrained Lagrangian dissipative contact dynamics

Constrained Lagrangian dissipative contact dynamics

A review on contact Hamiltonian and Lagrangian systems

Skinner-Rusk formalism for k-contact systems

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