2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73642The 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.33 pagesDynamical Systems34K13, 34K20, 37G15, 53D20text