Constrained Lagrangian dissipative contact dynamics

TL;DR

This paper demonstrates that contact dynamics derived from the Herglotz variational principle can be formulated as constrained Lagrangian systems with dissipation, unifying different approaches to dissipative contact systems.

Contribution

It introduces a novel formulation of contact nonholonomic and vakonomic systems as constrained Lagrangian systems with a dissipative variable, linking variational principles with dissipative dynamics.

Findings

Contact dynamics can be described as constrained Lagrangian systems.

Energy variation and dissipative quantities are derived within this framework.

Unification of contact nonholonomic and vakonomic systems under a common variational approach.

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.