# American Institute of Mathematical Sciences

December  2013, 5(4): 445-472. doi: 10.3934/jgm.2013.5.445

## Tulczyjew triples: From statics to field theory

 1 Physics Department, University of Warsaw, Hoża 69, 00-681 Warszawa, Poland 2 Polish Academy of Sciences, Institute of Mathematics, Śniadeckich 8, P.O. Box 21, 00-956 Warsaw

Received  April 2013 Revised  September 2013 Published  December 2013

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.
Citation: Katarzyna Grabowska, Janusz Grabowski. Tulczyjew triples: From statics to field theory. Journal of Geometric Mechanics, 2013, 5 (4) : 445-472. doi: 10.3934/jgm.2013.5.445
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