Homotopy operators for the variational bicomplex, representations of the Euler-Lagrange complex, and the Helmholtz-Sonin conditions

DOI10.1134/S1995080209020036zbMath1177.49056MaRDI QIDQ1033681

Mike Crampin, David J.Saunders

Publication date: 10 November 2009

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

variational bicomplexhomotopy operatorEuler-Lagrange complexHelmholtz-Sonin equationshorizontal differential

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Jets in global analysis (58A20) Inverse problems in optimal control (49N45)

Related Items (3)

Lepage equivalents and the variational bicomplex ⋮ Unnamed Item ⋮ Thirty years of the inverse problem in the calculus of variations

Cites Work

• The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. I: The linear theory
• A global version of the inverse problem of the calculus of variations
• Equivalence and the Cartan form
• Representation of the variational sequence by differential forms
• Higher-order differential equations and higher-order lagrangian mechanics
• An alternative approach to the Cartan form in Lagrangian field theories
• On the Helmholtz operator for Euler morphisms
• Global variational theory in fibred spaces
• Variational sequences
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