Grabowska, Katarzyna; Grabowski, Janusz Tulczyjew triples: from statics to field theory. (English) Zbl 1357.70016 J. Geom. Mech. 5, No. 4, 445-472 (2013). Summary: A geometric approach to dynamical equations of physics, based on the idea of the Tulczyjew triple, is presented. We show the evolution of these concepts, starting with the roots lying in the variational calculus for statics, through Lagrangian and Hamiltonian mechanics, and ending with Tulczyjew triples for classical field theories illustrated with a few important examples. Cited in 7 Documents MSC: 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 70G75 Variational methods for problems in mechanics 58A20 Jets in global analysis 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 53D05 Symplectic manifolds (general theory) 58A32 Natural bundles Keywords:Tulczyjew triple; classical field theory; Lagrange formalism; Hamiltonian formalism; variational calculus PDFBibTeX XMLCite \textit{K. Grabowska} and \textit{J. Grabowski}, J. Geom. Mech. 5, No. 4, 445--472 (2013; Zbl 1357.70016) Full Text: DOI arXiv