2023/04/03 by Xavier Rivas, Rivas, Xavier, Modesto Salgado +3 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #35R01 #53C15 #53D10 #70G45 #70S05 #70S10 #Elasticity and Material Modeling #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2304.00833
openalex publication_date 2023/04/03 · openalex created_date 2023/04/06 · openalex updated_date 2026/08/01
It is well known that k-contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the k-contact Euler-Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the k-contact Euler-Lagrange equations written in terms of k-vector fields and sections and provide new results relating the solutions in both approaches. We also study different kind of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and k-contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyse the relation between k-contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example.