A $k$-contact Lagrangian formulation for nonconservative field theories

Abstract

We present a geometric Lagrangian formulation for first-order field theories with dissipation. This formulation is based on the $k$-contact geometry introduced in a previous paper, and gathers contact Lagrangian mechanics with $k$-symplectic Lagrangian field theory together. We also study the symmetries and dissipation laws for these nonconservative theories, and analyze some examples.

arXiv commentarXiv admin note: text overlap with arXiv:1905.07354

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Cited by in corpus (15)

• Multicontact formulation for non-conservative field theories
• Unified Lagrangian-Hamiltonian formalism for contact systems
• Symmetries, conservation and dissipation in time-dependent contact systems
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Contact Lie systems
• Nonautonomous k-contact field theories
• Contact Lagrangian systems subject to impulsive constraints
• The Herglotz variational principle for dissipative field theories
• Application of Herglotz's Variational Principle to Electromagnetic Systems with Dissipation
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
• Practical Introduction to Action-Dependent Field Theories
• When action is not least for systems with action-dependent Lagrangians
• Constrained Lagrangian dissipative contact dynamics
• Skinner-Rusk formalism for k-contact systems
• Brackets in multicontact geometry and multisymplectization