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Tulczyjew triples: from statics to field theory. (English) Zbl 1357.70016

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.

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
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