The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems Dong Eui Chang, Anthony M. Bloch, Naomi E. Leonard, Jerrold E. Marsden and Craig A. Woolsey ESAIM: COCV, 8 (2002) 393-422 Published online: 15 August 2002 DOI: 10.1051/cocv:2002045