The inverse problem in the calculus of variations: new developments

DOI10.2478/cm-2021-0008zbMath1487.37072arXiv2001.06771OpenAlexW3163064398MaRDI QIDQ2236376

Thoan Do, Geoff Prince

Publication date: 22 October 2021

Published in: Communications in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06771

zbMATH Keywords

inverse problemcalculus of variationsexterior differential systemsHelmholtz conditionsLagrangian system

Mathematics Subject Classification ID

Exterior differential systems (Cartan theory) (58A15) Inverse problems in optimal control (49N45) Lagrange's equations (70H03) Action-minimizing orbits and measures for finite-dimensional Hamiltonian and Lagrangian systems; variational principles; degree-theoretic methods (37J51) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06)

Related Items (2)

Linear connections and shape maps for second order ODEs with and without constraints ⋮ Almost every path structure is not variational

Cites Work

• The inverse problem in the calculus of variations and the geometry of the tangent bundle
• The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations
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• Jacobi fields and linear connections for arbitrary second-order ODEs.
• The inverse problem of the calculus of variations: The use of geometrical calculus in Douglas’s analysis
• The Helmholtz conditions revisited. A new approach to the inverse problem of Lagrangian dynamics
• A geometrical version of the Helmholtz conditions in time-dependent Lagrangian dynamics
• An EDS approach to the inverse problem in the calculus of variations
• The inverse problem of the calculus of variations for ordinary differential equations
• Towards a geometrical understanding of Douglas's solution of the inverse problem of the calculus of variations
• Lagrangians for spherically symmetric potentials
• Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations
• On the inverse problem of the calculus of variations
• New progress in the inverse problem in the calculus of variations
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