Generalized virial theorem for contact Hamiltonian systems
Abstract
We formulate and study a generalized virial theorem for contact Hamiltonian systems. Such systems describe mechanical systems in the presence of simple dissipative forces such as Rayleigh friction, or the vertical motion of a particle falling through a fluid (quadratic drag) under the action of constant gravity. We find a generalized virial theorem for contact Hamiltonian systems which is distinct from that obtained earlier for the symplectic case. The `contact' generalized virial theorem is shown to reduce to the earlier result on symplectic manifolds as a special case. Various examples of dissipative mechanical systems are discussed. We also formulate a generalized virial theorem in the contact Lagrangian framework.
Cite
@article{arxiv.2301.09355,
title = {Generalized virial theorem for contact Hamiltonian systems},
author = {Aritra Ghosh},
journal= {arXiv preprint arXiv:2301.09355},
year = {2026}
}
Comments
v1: Preliminary version; v2: Revised version, references added; v3: Minor changes; v4: This version corrects typos, notational issues, minor technical errors, and references, and adds clarifying remarks