Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems
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arXiv
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| Format: | Preprint |
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2026
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| author | Gonçalves, Tânia M. N. Torres, Delfim F. M. Frederico, Gastão S. F. |
| author_facet | Gonçalves, Tânia M. N. Torres, Delfim F. M. Frederico, Gastão S. F. |
| contents | 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 $SO^+(1,2)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_29065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems Gonçalves, Tânia M. N. Torres, Delfim F. M. Frederico, Gastão S. F. Differential Geometry Mathematical Physics 53A55, 58E30, 70H03 (Primary) 49S05, 70G65, 70H33 (Secondary) 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 $SO^+(1,2)$. |
| title | Invariantised Euler-Lagrange equations and conserved quantities for nonconservative Herglotz variational problems |
| topic | Differential Geometry Mathematical Physics 53A55, 58E30, 70H03 (Primary) 49S05, 70G65, 70H33 (Secondary) |
| url | https://arxiv.org/abs/2605.29065 |