  The idea of dissipative mechanical system with delay is proposed. The paper
studies the phenomenon of dissipation with delay for Euler-Poincare systems on
Lie algebras or equivalently, for Lie-Poisson systems on the duals of Lie
algebras. The study was suggested by the work [2] and it is ended with a
discussion regarding the stability and the Hopf bifurcations for the free rigid
body with delay.
