Time-dependent contact mechanics
Manuel de León, Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz‐Lecanda, Xavier Rivas
Abstract
Abstract Contact 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.
Topics & Concepts
Dissipative systemSubmanifoldRotation formalisms in three dimensionsHolonomic constraintsHolonomicContact geometryLagrangianConstraint (computer-aided design)MathematicsGeometric mechanicsHamiltonian (control theory)Applied mathematicsClassical mechanicsComputer scienceMathematical analysisGeometryPhysicsMathematical optimizationAnalytical mechanicsArtificial intelligenceQuantumQuantum mechanicsQuantum dynamicsDynamics and Control of Mechanical SystemsElasticity and Material ModelingContact Mechanics and Variational Inequalities