On a global Lagrangian construction for ordinary variational equations on 2-manifolds

On a global Lagrangian construction for ordinary variational equations on 2-manifolds

J. Math. Phys. 60, 092902 (2019) Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic nature. A new constructive meth...

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Bibliographic Details
Main Authors: Urban, Zbyněk, Volná, Jana
Format: Journal Article
Language:English
Published: 11-12-2018
Subjects:
Mathematics - Algebraic Topology
Mathematics - Differential Geometry
Online Access:Get full text
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Summary:J. Math. Phys. 60, 092902 (2019) Locally variational systems of differential equations on smooth manifolds, having certain de Rham cohomology group trivial, automatically possess a global Lagrangian. This important result due to Takens is, how-ever, of sheaf-theoretic nature. A new constructive method of finding a global Lagrangian for second-order ODEs on 2-manifolds is described on the basis of solvability of exactness equation for Lepage 2-forms, and the top-cohomology theorems. Examples from geometry and mechanics are discussed.
DOI:10.48550/arxiv.1812.04270