New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
Jordi Gaset, Xavier Gràcia, Miguel C. Muñoz-Lecanda, Xavier Rivas, Narciso Román-Roy
Abstract
We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented Lagrangian formalisms, studying their equivalence. We define several kinds of symmetries for contact dynamical systems, as well as the notion of dissipation laws, prove a dissipation theorem and give a way to construct conserved quantities. Some well-known examples of dissipative systems are discussed.
Topics & Concepts
Dissipative systemDissipationMechanical systemHomogeneous spaceLagrangianDissipative operatorRotation formalisms in three dimensionsClassical mechanicsHamiltonian (control theory)Hamiltonian systemPhysicsHamiltonian mechanicsConserved quantityFormalism (music)Dynamical systems theoryMathematical physicsMathematicsCovariant Hamiltonian field theoryTheoretical physicsNoether's theoremAnalytical dynamicsInverse problem for Lagrangian mechanicsControl and Stability of Dynamical SystemsContact Mechanics and Variational InequalitiesNumerical methods for differential equations