The version of record is available online at: http://dx.doi.org/10.1007/s00605-022-01767-1Contact geometry allows us 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.We acknowledge fruitful discussions and comments from our colleague Narciso
Román-Roy. MdL acknowledges the financial support of the Ministerio de Ciencia e Innovación (Spain),
under grants PID2019-106715GB-C2, “Severo Ochoa Programme for Centres of Excellence in R&D”
(CEX2019-000904-S) and EIN2020-112107. JG, XG, MCML and XR acknowledge the financial support
of the Ministerio de Ciencia, Innovación y Universidades (Spain), project PGC2018-098265-B-C33.Peer ReviewedPostprint (author's final draft
