Generalized virial theorem for contact Hamiltonian systems

TL;DR

This paper develops a generalized virial theorem for contact Hamiltonian systems, extending classical results to dissipative systems like those with friction or fluid drag, and connects it to the symplectic case.

Contribution

It introduces a novel virial theorem for contact Hamiltonian systems, broadening the theoretical framework to include dissipative forces and linking it to existing symplectic results.

Findings

Derived a generalized virial theorem for contact Hamiltonian systems.

Showed the theorem reduces to the classical symplectic case.

Discussed applications to various dissipative mechanical 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.