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    Controllability of Lie-Poisson Reduced Dynamics

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    TR_97-59.pdf (315.6Kb)
    No. of downloads: 676

    Date
    1997
    Author
    Manikonda, Vikram
    Krishnaprasad, Perinkulam S.
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    Abstract
    In this paper we present sufficient conditions for controllability of Lie-Poisson 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 field (of the reduced system) is weakly positively Poisson stable (WPPS). The WPPS nature of the drift vector field along with the Lie algebra rank condition is used to show controllability of the reduced system. We discuss the dynamics, Lie-Poisson reduction, and controllability of hovercraft, spacecraft and underwater vehicles, all treated as rigid bodies.
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    http://hdl.handle.net/1903/5877
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