Dr. Yildirim Hurmuzlu

01-13-2001, 02:32 PM

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

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