Contact Hamiltonian systems with nonholonomic constraints

TL;DR

This paper develops a theoretical framework for contact Hamiltonian systems with nonholonomic constraints, deriving their dynamics via a variational principle and introducing a new nonholonomic bracket structure.

Contribution

It introduces a novel approach to nonholonomic contact systems by deriving their dynamics from Herglotz's variational principle and defining an almost Jacobi bracket.

Findings

Nonholonomic dynamics are projections of unconstrained Hamiltonian vector fields.

A new nonholonomic bracket is constructed, forming an almost Jacobi structure.

The framework extends contact Hamiltonian theory to constrained systems.

Abstract

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.