The purpose of this paper is to show that the method of controlledLagrangians and its Hamiltonian counterpart (based on the notionof passivity) are equivalent under rather general hypotheses. Westudy the particular case of simple mechanical control systems(where the underlying Lagrangian is kinetic minus potentialenergy) subject to controls and external forces in some detail.The equivalence makes use of almost Poisson structures (Poissonbrackets that may fail to satisfy the Jacobi identity) on theHamiltonian side, which is the Hamiltonian counterpart of a classof gyroscopic forces on the Lagrangian side.
