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    Aspects of Geometric Mechanics and Control of Mechanical Systems

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    1995f_letter.pdf (1.107Mb)
    Date
    1995
    Author
    Lewis, Andrew D.
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    Abstract
    Many interesting control systems are mechanical control systems. In spite of

    this, there has not been much effort to develop methods which use the special

    structure of mechanical systems to obtain analysis tools which are

    suitable for these systems. In this thesis we take the first steps towards a

    methodical treatment of mechanical control systems.

    First we begin to develop a framework for analysis of certain classes of

    mechanical control systems. In the Lagrangian formulation we study "simple

    mechanical control systems" whose Lagrangian is "kinetic energy minus

    potential energy." We propose a new and useful definition of

    controllability for these systems and obtain a computable set of conditions

    for this new version of controllability. We also obtain decompositions of

    simple mechanical systems in the case when they are not controllable. In the

    Hamiltonian formulation we study systems whose control vector fields are

    Hamiltonian. We obtain decompositions which describe the controllable and

    uncontrollable dynamics. In each case, the dynamics are shown to be

    Hamiltonian in a suitably general sense.

    Next we develop intrinsic descriptions of Lagrangian and Hamiltonian

    mechanics in the presence of external inputs. This development is a first

    step towards a control theory for general Lagrangian and Hamiltonian

    control systems. We also study systems with constraints. We first give a

    thorough overview of variational methods including a comparison of the

    "nonholonomic" and "vakonomic" methods. We also give a generalised

    definition for a constraint and, with this more general definition, we are

    able to give some preliminary controllability results for constrained systems.
    URI for this record
    http://hdl.handle.net/1974/39
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