On Geometrical Couplings of Dissipation and Curl Forces

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.

Dedicated to Sir Michael Berry on his 80th birthday with great respect and admiration

References in corpus (3)

• The principle of stationary nonconservative action for classical mechanics and field theories
• A review on contact Hamiltonian and Lagrangian systems
• On Extensions, Lie-Poisson Systems, and Dissipations

Cited by in corpus (1)

• Geometric Hamilton-Jacobi theory for systems with external forces