  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.
