Contact geometric mechanics: the Tulczyjew triples
| Autor: | Grabowska, Katarzyna, Grabowski, Janusz |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Adv. Theor. Math. Phys. Volume 28, Number 2, 599-654, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4310/atmp.240914022224 |
| Popis: | 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. Comment: 35 pages, minor changes, a few references added, to appear in Advances in Theoretical and Mathematical Physics |
| Databáze: | arXiv |
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