Time-dependent contact mechanics
Manuel de Le\'on, Jordi Gaset, Xavier Gr\`acia, Miguel Carlos, Mu\~noz-Lecanda, Xavier Rivas
TL;DR
This paper introduces cocontact manifolds to model time-dependent contact systems, developing Hamiltonian and Lagrangian formalisms, including a constraint algorithm for singular cases, with applications to systems with holonomic constraints and numerical examples.
Contribution
It presents a novel geometric framework for time-dependent contact mechanics using cocontact manifolds, extending existing formalisms to singular systems.
Findings
Development of Hamiltonian and Lagrangian formalisms for cocontact systems
A constraint algorithm for singular contact systems
Numerical simulations demonstrating the theory
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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Taxonomy
TopicsDynamics and Control of Mechanical Systems · Advanced Numerical Analysis Techniques · Contact Mechanics and Variational Inequalities