Higher-order variational problems of Herglotz type

DOI10.1007/s10013-013-0048-9zbMath1305.49025arXiv1309.6518OpenAlexW3101698045WikidataQ57650705 ScholiaQ57650705MaRDI QIDQ484478

Natália Martins, Simão P. S. Santos, Delfim F. M. Torres

Publication date: 7 January 2015

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

Full work available at URL: https://arxiv.org/abs/1309.6518

zbMATH Keywords

natural boundary conditionsEuler-Lagrange differential equationsgeneralized calculus of variations

Mathematics Subject Classification ID

Control problems involving ordinary differential equations (34H05) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (16)

Variational problem of Herglotz type for Birkhoffian system and its Noether's theorems ⋮ Noether's theorem for fractional Birkhoffian system of Herglotz type with time delay ⋮ Adiabatic invariants for disturbed fractional Hamiltonian system in terms of Herglotz differential variational principle ⋮ Fractional Herglotz variational principles with generalized Caputo derivatives ⋮ Noether currents for higher-order variational problems of Herglotz type with time delay ⋮ Fractional Herglotz variational problems of variable order ⋮ Noether’s theorem for Herglotz type variational problems utilizing complex fractional derivatives ⋮ Herglotz-type principle and first integrals for nonholonomic systems in phase space ⋮ Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter ⋮ Fractional variational principle of Herglotz ⋮ Noether's theorem for variational problems of Herglotz type with real and complex order fractional derivatives ⋮ Variational and optimal control approaches for the second-order Herglotz problem on spheres ⋮ Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem ⋮ Noether's theorem for higher-order variational problems of Herglotz type ⋮ Optimality conditions involving the Mittag-Leffler tempered fractional derivative ⋮ A non-standard class of variational problems of Herglotz type

Cites Work

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• Calculus of variations on time scales with nabla derivatives
• First Noether-type theorem for the generalized variational principle of Herglotz
• Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations
• Necessary optimality conditions for higher-order infinite horizon variational problems on time scales
• Second Noether-type theorem for the generalized variational principle of Herglotz
• Generalized variational principle of Herglotz for several independent variables. First Noether-type theorem
• The Herglotz Algorithm for Constructing Canonical Transformations
• Extension of the Herglotz Algorithm to Nonautonomous Canonical Transformations

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