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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.15679 |
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Table of 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.