Discrete variational calculus for double-bracket dissipation
Abstract
Discrete variational methods show excellent performance in numerical simulations of mechanical systems. In this paper, we adapt discrete variational integrators for the case of mechanical systems with double-bracket dissipation. In particular, we will work with forced Euler-Poincar\'e and forced Lie-Poisson systems, and the case of interest for us will be when the coadjoint orbits remain invariant, but the energy is decreasing along the orbit. This particular kind of dissipative system appears in various physical systems such as satellites with dampers, geophysical fluids, plasma physics and stellar dynamics. The proposed geometric integrator preserves the coadjoint orbits exactly. We highlight the advantages of this feature by comparing it with other general-purpose methods (including higher-order ones) across different numerical simulations.
Keywords
Cite
@article{arxiv.2604.26049,
title = {Discrete variational calculus for double-bracket dissipation},
author = {Anthony Bloch and Sebastián J. Ferraro and David Martín de Diego and Shreyas Bharadwaj},
journal= {arXiv preprint arXiv:2604.26049},
year = {2026}
}