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arXiv · 2606.05550

Variational Inverse Problems for Second Order ODEs with and without Constraints

G. E. Prince·T. Mestdag·D. Martin de Diego
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Abstract

Many physical systems with or without nonholonomic constraints have a Lagrangian description. In the first case, the Lagrangian model can be represented by second-order ODEs that are constrained to a submanifold of velocities; in the latter case the ODEs are unconstrained. In this paper, using geometric techniques, we address the more general inverse problem: ``When can a given constrained or unconstrained system of second order ODEs on a manifold be the representation of a Lagrangian model?''. We show that the constrained case has many more ambiguities and complexities than its well-understood, unconstrained counterpart.

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BibTeXRIS

G. E. Prince, T. Mestdag, D. Martin de Diego. 2026-06-04. Variational Inverse Problems for Second Order ODEs with and without Constraints. https://arxiv.org/abs/2606.05550

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