[ATM] Moments of Torque, frustration, and insanity :)

[martin.cibulski at degussa.com (martin.cibulski@degussa.com)]

James,

> The angular acceleration at time 0 is now the angular velocity at time 1.
At
> this point I need to introduce a new procedure which will compare the
angular
> velocity for each point on the lap with the angular velocity of the
mirror
> beneath this point.  The result of this new comparision will be a change
in sign
> for each element representing the forces on the lap.  Calculate new
angular
> acceleration, add this to previous angular velocity, repeat....

I don't think you need a new procedure here if the first procedure can
handle tool rotation too.

The procedure should always calculate relative motion of the mirror under
the tool for each contact point to get the friction force vectors.
The X and Y components of both motion vectors (mirror's and tool's surface
element) can be subtracted to get the relative motion.
The motion vector of a surface element at a position (X,Y) from the pivot
point (mirror's / tool's center) is easy to calculate as:
Vx = -omega * (Y - Ycenter)
Vy = +omega * (X - Xcenter)
Omega (rad/sec) is positive in a CCW rotation here, X is right, Y is up.

The relative motion of the tool on the mirror is:
Vxrel = Vxtool - Vxmirror
Vyrel = Vytool - Vymirror
(must be calculated for every contact point in the array)

> Given small steps in time and a reasonable guess at the force of
friction,
> eventauly the loop will stabilize to a static angular velocity...

Yes, it should.
A higher order integration algorithm (Runge Kutta) will give better
results here. For first experiments a first order integration with a
smaller time step size should work too.

Regards,
Martin
http://martin.cibulski.bei.t-online.de