Constrained Lagrangian dissipative contact dynamics

Abstract

We show that the contact dynamics obtained from the Herglotz variational principle can be described as a constrained nonholonomic or vakonomic ordinary Lagrangian system depending on a dissipative variable with an adequate choice of one constraint. As a consequence we obtain the dynamics of contact nonholonomic and vakonomic systems as ordinary variational calculus with constraints on a Lagrangian with a dissipative variable. The variation of the energy and the other dissipative quantities are also obtained giving the usual results.

32 pp. New sections are added (3.4, 4.3, 5.5). Other minor changes. The bibliography is updated

References in corpus (11)

• Contact Hamiltonian Systems
• New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries
• Contact manifolds and dissipation, classical and quantum
• Infinitesimal symmetries in Contact Hamiltonian systems
• A contact geometry framework for field theories with dissipation
• Singular Lagrangians and precontact Hamiltonian Systems
• Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
• A $k$-contact Lagrangian formulation for nonconservative field theories
• An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
• Unified Lagrangian-Hamiltonian formalism for contact systems
• Higher-order contact mechanics