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A K-contact Lagrangian formulation for nonconservative field theories

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2002.10458.pdf (278,2Kb)
 
10.1016/S0034-4877(21)00041-0
 
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hdl:2117/365729

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Gaset Rifà, Jordi
Gràcia Sabaté, Francesc XavierMés informacióMés informacióMés informació
Muñoz Lecanda, Miguel CarlosMés informacióMés informació
Rivas Guijarro, Xavier
Román Roy, NarcisoMés informacióMés informacióMés informació
Document typeArticle
Defense date2021-06-01
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 3.0 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain
ProjectGEOMETRIA-FISICA-CONTROL Y APLICACIONES (AEI-PGC2018-098265-B-C33)
Abstract
Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper where we introduced the notion of k-contact structure, and obtained a modified version of the De Donder–Weyl equations of covariant Hamiltonian field theory. In this paper we continue this study by presenting a k-contact Lagrangian formulation for nonconservative field theories. The Lagrangian density is defined on the product of the space of k-velocities times a k-dimensional Euclidean space with coordinates sa, which are responsible for the dissipation. We analyze the regularity of such Lagrangians; only in the regular case we obtain a k-contact Hamiltonian system. We study several types of symmetries for k-contact Lagrangian systems, and relate them with dissipation laws, which are analogous to conservation laws of conservative systems. Several examples are discussed: we find contact Lagrangians for some kinds of second-order linear partial differential equations, with the damped membrane as a particular example, and we also study a vibrating string with a magnetic-like term.
CitationGaset, J. [et al.]. A K-contact Lagrangian formulation for nonconservative field theories. "Reports on mathematical physics", 1 Juny 2021, vol. 87, núm. 3, p. 347-368. 
URIhttp://hdl.handle.net/2117/365729
DOI10.1016/S0034-4877(21)00041-0
ISSN0034-4877
Publisher versionhttps://www.sciencedirect.com/science/article/abs/pii/S0034487721000410
Other identifiershttps://arxiv.org/pdf/2002.10458.pdf
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