Time-dependent contact mechanics

Jordi Gaset; Manuel de Le\'on; Miguel Carlos Mu\~noz-Lecanda; Xavier Gr\`acia; Xavier Rivas

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arxiv 2205.09454 v2 pith:AMFKQJKF submitted 2022-05-19 math-ph math.MPmath.SG

Time-dependent contact mechanics

Manuel de Le\'on , Jordi Gaset , Xavier Gr\`acia , Miguel Carlos Mu\~noz-Lecanda , Xavier Rivas This is my paper

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keywords contactsingularsystemstime-dependentcasedescriberegularsome

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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.

Time-dependent contact mechanics

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