Thank you for this explanation. It's good.
I'm trying to find out the platform finish line velocity. I'm sure it'll close
to zero, but the platform may not stop. Why? Because even if follow law of
momentum conservation, the bodies on phases 1 and 3 have different mass.
Thanks anyway. I'll continue work with this problem and I'll put more details
on knoll site.

--- In mathforfun@yahoogroups.com, "video_ranger" <video_ranger@...> wrote:
>
> --- In mathforfun@yahoogroups.com, "abelov0927" <abelov0927@> wrote:
> >
> > By 'model', I just want to describe behavior of this system. All laws of
classical mechanic should be preserved.
> > Initial platform velocity is zero V0=0. Will platform return to this initial
velocity after all? This is what I'm looking for.
> > Is it physically possible calculating this on math modeling?
> >
> > Thank you
> >
> >
>
> If the platform is completely free to move (say floating in outer space)
momentum conservation requires that it will end up with a positive forward
velocity V=((M+nm)/nm)v. Kinetic energy is not conserved because as each link
slaps down on the surface some energy is converted to heat.
>
> For a full ring rolling at constant velocity there's no horizontal force
between the bottom of the ring and the surface but that requires the ring to be
balanced (rotationally symmetric). As links become missing from the circle
that's no longer true so the succeeding links that hit the surface do have a
forward pull on them accelerating the platform forward.
>
> But offhand I'm not sure how to calculate the detailed dynamics that describe
how the platform goes from 0 velocity to its final velocity (the system has n
degrees of freedom so it's more complicated than a simple rolling ring with 1
degree of freedom).
>