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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
equilibrium
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
anywhere.
According to the theory of nonlinear dynamical systems, the dynamic
equilibria in running and walking are described as limit cycles. The limit
cycle
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
parameters.
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 : hurmuzlu@seas.smu.edu
web : http://cyborg.seas.smu.edu/~hurmuzlu/
====================================
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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
equilibrium
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
anywhere.
According to the theory of nonlinear dynamical systems, the dynamic
equilibria in running and walking are described as limit cycles. The limit
cycle
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
parameters.
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 : hurmuzlu@seas.smu.edu
web : http://cyborg.seas.smu.edu/~hurmuzlu/
====================================
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To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
For information and archives: http://isb.ri.ccf.org/biomch-l
---------------------------------------------------------------