The geometry of ordinary variational equations

DOI10.1007/BFb0093438zbMath0936.70001OpenAlexW1564260361MaRDI QIDQ1376249

Olga Krupková

Publication date: 17 December 1997

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bfb0093438

zbMATH Keywords

Euler-Lagrange equationsHamilton-Jacobi equationHamiltonian systemssymmetriessingular Lagrangian systemsLagrangian dynamicsLegendre transformationinverse problem of calculus of variationsjet prolongationfibre manifoldsEuler-Lagrange distributionHamilton extremalsHamilton-Jacobi distributionholonomic sectionsintegral sectionsJacobi complete integralLepagean-formquasi-configuration spacesemiregular Lagrangian systems

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Hamilton-Jacobi equations in mechanics (70H20) Optimality conditions for problems involving ordinary differential equations (49K15) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Lagrange's equations (70H03) Higher-order theories for problems in Hamiltonian and Lagrangian mechanics (70H50) Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems (70-02)

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