Re: [Phys-l] Equations (causal relationship)

[John Denker <jsd@av8n.com>]

Michael Edmiston wrote:

> > Imagine three uniaxial translation stages, of the kind you see all
> > over the place on optical tables.  Stack three of them together,
> > one atop the other.  The particle of interest is attached to the
> > top of the stack.
> >
> > Arrange that the first stage has its axis aligned with force F1, the
> > second one aligned with force F2, and  the third one aligned with
> > force F3.
> >
> > Arrange that the first one accelerates at the rate F1/m, the second
> > one at the rate F2/m, and the third one at the rate F3/m.
> >
> > The three accelerations are nonzero.  They add to zero.  You can
> > see the stages moving, even though the particle does not move.
>
>
> Yes, but... I think in this case there are no forces exerted on the 
> particle.  Not only is there no net force on the particle, there are no 
> forces at all.  I think your imagination has come up with a scenario 
> that does not accomplish the desired goal.

Sorry, I wasn't clear enough.  I imagined (and continue to imagine) that
the three forces *were* acting.

Meanwhile, I want the position of the particle to be "controlled" by
the translation stages.  The force connecting the particle to the
top stage is one of the forces that must be considered;  call it Fi
without loss of generality, where i can be 1, 2, or 3;  I do not
insist that Fi/m be the acceleration of the top stage ... it could
be the acceleration of one of the other stages.

The other two forces are attached to nearby struts, not to the stack
of stages.

Clear enough?