Albuquerque , New Mexico , June 4 - 6 , 1997 Controllability of Lie - Poisson Reduced Dynamics 1
نویسنده
چکیده
In this paper we present suucient conditions for the controllability of the reduced dynamics of a class of mechanical systems with symmetry. We prove conditions (boundedness of coadjoint orbits and existence of a radially unbounded Lyapunov function) under which the drift vector eld (of the reduced system) is weakly positively Poisson stable (WPPS). The WPPS nature of the drift vector eld along with the Lie algebra rank condition is used to show controllability of the reduced system. We discuss the dynamics, Lie-Poisson reduction, and control-lability of hovercraft and underwater vehicles, all treated as rigid bodies.
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