Muñoz Masqué, J.; Rosado María, M. Eugenia Invariant variational problems on linear frame bundles. (English) Zbl 1029.70013 J. Phys. A, Math. Gen. 35, No. 8, 2013-2036 (2002). The authors describe the Hamiltonian structure of actions defined by Lagrangians corresponding to the natural basis of diff \(M\)-invariant Lagrangians on a 1-jet bundle of linear frames of a manifold \(M\). It is shown that there are two types of variational problems. The corresponding field equations are obtained, and it is shown that these are underdetermined nonlinear systems of partial differential equations. Infinitesimal symmetries and Noether invariants of the systems are also studied, and it is shown that the Noether invariant of every vertical symmetry vanishes. Reviewer: Mohammad Khorrami (Zanjan) Cited in 5 Documents MSC: 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics 58Z05 Applications of global analysis to the sciences 70H30 Other variational principles in mechanics Keywords:linear frames; infinitesimal symmetries; variational problems; Hamiltonian structure; invariant Lagrangians; jet bundle; manifold; Noether invariants; vertical symmetry PDFBibTeX XMLCite \textit{J. Muñoz Masqué} and \textit{M. E. Rosado María}, J. Phys. A, Math. Gen. 35, No. 8, 2013--2036 (2002; Zbl 1029.70013) Full Text: DOI