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Re: Inverse Dynamics

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  • Re: Inverse Dynamics

    I would like to comment on the remarks of Professor Feldman
    regarding the equilibrium states in walking and running.

    > 1. Where are the equilibrium states in walking and running?
    > Response. A single step is a transition from one postural (equilibrium)
    > state to another. One can also say that a step results from changes in
    > specific parameters that transform the equilibrium configuration of the
    > body in such a way that eventually the body establishes approximately
    > the same (initial) posture but in another part of external space.

    The equilibrium in running/walking is a dynamic one. One cannot describe it
    as a transition from one postural equilibrium to another. The postural
    is a static one (I assume that it means the biped is standing). By
    definition, a static
    equilibrium is "static". So, once a system is in a static equilibrium , it
    should not be moving

    According to the theory of nonlinear dynamical systems, the dynamic
    equilibria in running and walking are described as limit cycles. The limit
    is a periodic motion that can repel (unstable) or attract (stable) other
    motions that start
    from neighboring initial conditions.

    In addition, there is one set of parameter values that are associated with
    each equilibrium
    state. The only things that vary in time are the state variables. Anything
    else that changes can
    be expressed as a function of these variables. One cannot have an
    equilibrium state that
    consists of transition from one equilibrium state to another by varying the

    Best regards,

    Yildirim Hurmuzlu

    Yildirim Hurmuzlu
    Professor of Mechanical Engineering
    Southern Methodist University
    Dallas, TX 75275

    Phone : (214) 768-3498
    Fax : (214) 768-1473
    e-mail :
    web :

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