The inverse problem of the calculus of variations: The use of geometrical calculus in Douglas’s analysis

DOI10.1090/S0002-9947-02-02994-XzbMath1038.37044MaRDI QIDQ2782668

Geoff Prince, Gerard Thompson, Willy Sarlet

Publication date: 8 April 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

inverse problemLagrangian systemsgeometrical calculus

Mathematics Subject Classification ID

Other variational principles in mechanics (70H30) Inverse problems in optimal control (49N45) Lagrange's equations (70H03) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (16)

An EDS approach to the inverse problem in the calculus of variations ⋮ Tangent bundle geometry induced by second order partial differential equations ⋮ On the inverse problem of the discrete calculus of variations ⋮ The Lagrangian order-reduction theorem in field theories ⋮ Freedom of \(h(2)\)-variationality and metrizability of sprays ⋮ The Inverse Problem of the Calculus of Variations and the Stabilization of Controlled Lagrangian Systems ⋮ An extension to the theory of controlled Lagrangians using the Helmholtz conditions ⋮ Inverse problem for Chaplygin's nonholonomic systems ⋮ Helmholtz conditions and symmetries for the time dependent case of the inverse problem of the calculus of variations ⋮ Lepage forms, closed 2-forms and second-order ordinary differential equations ⋮ The inverse problem in the calculus of variations: new developments ⋮ Unnamed Item ⋮ Contact symmetries of the Helmholtz form ⋮ New progress in the inverse problem in the calculus of variations ⋮ On nonholonomic systems and variational principles ⋮ FINSLER METRIZABLE ISOTROPIC SPRAYS AND HILBERT’S FOURTH PROBLEM

Cites Work

• Unnamed Item
• Derivations of differential forms along the tangent bundle projection
• The integrability conditions in the inverse problem of the calculus of variations for second-order ordinary differential equations
• Sur le problème inverse du calcul des variations : existence de lagrangiens associés à un spray dans le cas isotrope. (On the inverse problem of the variational calculus: existence of Lagrangians associated with a spray in the isotropic case.)
• Derivations of differential forms along the tangent bundle projection. II
• Derivations of forms along a map: The framework for time-dependent second-order equations
• Local vanishing of characteristic cohomology
• 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
• Geometric characterization of separable second-order differential equations
• Solution of the Inverse Problem of the Calculus of Variations

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