You could use linear density (mass per unit length) if you want the mass. You only need the mass if you want accurate calculation of the speed in real units. If you just want the motion around the spindle, you can set the mass=1 arbitrary unit and integrate the magnitude of F_perp as you go around to determine the relative speed at any given point.

you can set the mass=1 arbitrary unit and integrate the magnitude of F_perp as you go around to determine the relative speed at any given point.

That's an interesting notion, although it's hard to see what the calculated speed would be relative to?

In as much as, whilst I have to enter a "known starting point" to the FEA, it does not necessarily follow that that starting point is stationary. The forces acting are the same regardless of the instantaneous velocities of the components they are acting upon, and they remain the same from beginning to end of the infinitesimally small time delta over which the integration runs.

So even if the result of the integration of F_perp came out as zero, it wouldn't mean that there was either no speed, nor no change in speed, simply that no change had occurred within that tending toward zero delta?

That means that the calculated forces will not have any affect within the time delta of the simulation; and thus will only take affect between simulations; which I think means that the FEA cannot tell me anything about the rate of change that will occur as a result of the forces it calculates?

At which point my brain hurts and I'm gonna sleep on it to see if this all still makes sense to me when I read it back in the morning; or if I've just thunk my way into a blind alley :)

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You're overthinking it. All you're trying to do is numerically integrate the accelerations over time to get the new position at any given time.

You can start with F=ma. Your system means that the motion is constrained to a circle, so all of the a's and v's will be angular accelerations and velocities.

Don't solve the forces at a uniform distribution of positions around the circle, solve them at a uniform distribution of times. To get the new position at each time, use the acceleration (a=F, since m=1)to get the velocity, then add v*t to your current position to get the new position (holding the current velocity for use next time, too. If you pick reasonably small time steps, this should work fine. If you solve it at uniform angles instead, you should be able to get away with interpolating. It doesn't matter if there's an initial angular velocity-- that would just be added to whatever you get.

In pseudocode I think all you need is:

$m_inverse=1  /* this could be chosen as arbitrarily small, like 0.000
+01 to get effectively smaller time steps) */
$v=0
$theta=0
while(!$done){
    ($F_x,$F_y)=ForceCalculator($theta)
    $F_perp=$F_x*sin(theta)+$F_y*cos($theta)
    $v=$v+$F_perp*$scale
    $theta=$theta+$v
}
[download]

And you just have to make $m_inverse small enough to make the motion from step to step differences small. This is equivalent to changing the mass.

EDIT: this is the same thing that salva said here: Re^7: [OT] Forces.