In this paper we develop a constructive approach to the determination of st
abilizing control laws for a class of Lagrangian mechanical systems with sy
mmetry - systems whose underlying dynamics are governed by the Euler-Poinca
re equations. This work extends our previous work on the stabilization of m
echanical control systems using the method of controlled Lagrangians. 7:he
guiding principle behind our methodology is to develop a class of stabilizi
ng feedback control laws which yield closed-loop dynamics that remain in La
grangian form. Using the methodology for Euler-Poincare systems, we analyse
stabilization of a satellite and an underwater vehicle controlled with mom
entum wheels. Copyright (C) 2001 John Wiley & Sons, Ltd.