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arXiv · 2605.29065

Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems

Tânia M. N. Gonçalves·Delfim F. M. Torres·Gastão S. F. Frederico
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Abstract

In this paper the structures of the generalised Euler-Lagrange equations and their associated conserved quantities are derived for one-dimensional Herglotz variational problems of order $n$. Their derivations use the framework of moving frames and invariant calculus of variations. The knowledge of these structures not only offers a geometric insight, it may provide a more efficient path for the determination of extremals. This is exemplified with a Herglotz problem invariant under the restricted Lorentz group $SO^+(1,2)$.

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Tânia M. N. Gonçalves, Delfim F. M. Torres, Gastão S. F. Frederico. 2026-05-27. Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems. https://arxiv.org/abs/2605.29065

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