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arXiv · 2209.03154

Contact geometric mechanics: the Tulczyjew triples

Katarzyna Grabowska·Janusz Grabowski
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Abstract

We propose a generalization of the classical Tulczyjew triple as a geometric tool in Hamiltonian and Lagrangian formalisms which serves for contact manifolds. The r\^ole of the canonical symplectic structures on cotangent bundles in Tulczyjew's case is played by the canonical contact structures on the bundles $J^1L$ of first jets of sections of line bundles $L\to M$. Contact Hamiltonians and contact Lagrangians are understood as sections of certain line bundles, and they determine (generally implicit) dynamics on the contact phase space $J^1L$. We also study a contact analog of the Legendre map and the Legendre transformation of generating objects in both contact formalisms. Several explicit examples are offered.

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BibTeXRIS

Katarzyna Grabowska, Janusz Grabowski. 2022-09-07. Contact geometric mechanics: the Tulczyjew triples. https://doi.org/10.4310/atmp.240914022224

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