On globally invariant Euler--Lagrange equations for curves
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918283048910848 |
|---|---|
| author | Kruglikov, Boris Schneider, Eivind Steneker, Wijnand |
| author_facet | Kruglikov, Boris Schneider, Eivind Steneker, Wijnand |
| contents | Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case the computation can be modified in several aspects. We will discuss relations with previous approaches and some foundational aspects.
The theory of invariant Euler-Lagrange equations was applied to curves with respect to the motion group in the Euclidean plane and space. We expand those computations to the next dimension four (Minkowski spacetime), which already exhibits computational challenges. We also provide formulas for other examples, namely the projective and conformal (Möbius) groups and relate to some recent applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On globally invariant Euler--Lagrange equations for curves Kruglikov, Boris Schneider, Eivind Steneker, Wijnand Differential Geometry Classical Analysis and ODEs 49Q20, 58E40, 70H03, 35A15, 37K05, 30C70 Invariant Lagrangians yield invariant Euler-Lagrange equations, and it was discussed in the literature how to compute those using various local methods. The focus of this paper is on global algebraic differential invariants. In this case the computation can be modified in several aspects. We will discuss relations with previous approaches and some foundational aspects. The theory of invariant Euler-Lagrange equations was applied to curves with respect to the motion group in the Euclidean plane and space. We expand those computations to the next dimension four (Minkowski spacetime), which already exhibits computational challenges. We also provide formulas for other examples, namely the projective and conformal (Möbius) groups and relate to some recent applications. |
| title | On globally invariant Euler--Lagrange equations for curves |
| topic | Differential Geometry Classical Analysis and ODEs 49Q20, 58E40, 70H03, 35A15, 37K05, 30C70 |
| url | https://arxiv.org/abs/2601.06985 |