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arXiv · 2205.09454

Time-dependent contact mechanics

Manuel de León·Jordi Gaset·Xavier Gràcia·Miguel Carlos Muñoz-Lecanda·Xavier Rivas
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Abstract

Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop the Hamiltonian and Lagrangian formalisms, both in the regular and singular cases. In the singular case, we present a constraint algorithm aiming to find a submanifold where solutions exist. As a particular case we study contact systems with holonomic time-dependent constraints. Some regular and singular examples are analyzed, along with numerical simulations.

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Manuel de León, Jordi Gaset, Xavier Gràcia, Miguel Carlos Muñoz-Lecanda, Xavier Rivas. 2022-05-19. Time-dependent contact mechanics. https://arxiv.org/abs/2205.09454

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