Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.15679 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911687944175616 |
|---|---|
| author | Scomparin, Mattia |
| author_facet | Scomparin, Mattia |
| contents | We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition between the kinetic matrices and the potential. For constant symmetric kinetic matrices, this condition reduces to a commutation relation with the Hessian of the potential, yielding an orthogonal spectral decomposition of the configuration space. The equations of motion then decouple into independent subsystems: generically in block-separated form, and completely when the spectrum is simple. Applications include the Sawada--Kotera system and an $n$-dimensional extension of the Hénon--Heiles model, where the classical integrable parameter regimes are recovered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral separation of variables from equivalent Lagrangian systems Scomparin, Mattia Mathematical Physics We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition between the kinetic matrices and the potential. For constant symmetric kinetic matrices, this condition reduces to a commutation relation with the Hessian of the potential, yielding an orthogonal spectral decomposition of the configuration space. The equations of motion then decouple into independent subsystems: generically in block-separated form, and completely when the spectrum is simple. Applications include the Sawada--Kotera system and an $n$-dimensional extension of the Hénon--Heiles model, where the classical integrable parameter regimes are recovered. |
| title | Spectral separation of variables from equivalent Lagrangian systems |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.15679 |