On Geometrical Couplings of Dissipation and Curl Forces

TL;DR

This paper introduces geometric frameworks to incorporate gyroscopic and dissipative forces into curl force systems, extending Lagrangian and Hamiltonian formalisms for non-conservative dynamics.

Contribution

It develops a metriplectic geometry and uses variational principles to formulate dissipative curl forces, broadening the theoretical understanding of non-conservative systems.

Findings

Presented a metriplectic geometric framework for dissipative curl forces

Formulated dissipative radial curl forces using the Herglotz principle

Extended the formulation to azimuthal curl forces with Galley's method

Abstract

In this paper, we present several geometric ways to incorporate gyroscopic and dissipative forces to curl forces. We first present a proper metriplectic geometry. Then, using the Herglotz principle and generalized Euler-Lagrange equation, we propose a formulation of dissipative radial curl forces. Finally, we extend our result to azimuthal curl force using Galley's method, which leads to a natural formulation for Lagrangian and Hamiltonian dynamics of generic non-conservative systems.