Re: Math for constant speed ellipse

Todd,

I think you kind of missed my point. The way I looked at your problem
was to pretend an ellipsoid is used in the place of a round wheel on
a vehicle like a unicycle.

Since the wheel is in frictional contact with the surface it rides
on, one can safely assume the tangential velocity is constant (your
goal).

If the ellipsoid "wheel" were driven at a constant RPM, the forward
velocity of the unicycle would span a 5:1 cyclic range using the
example.

The question becomes "how should you vary the RPM of the
ellipsoid "wheel" to keep its centroid forward velocity constant?" in
this thought experiment.

The "9 degree" business was simply a means to set up enough data
points to glean information of what that relationship is between rate
of angular change and tangential velocity, so as to keep tangential
velocity constant.

That presented itself intuitively (to me anyway) as the "y" position
of the centroid of the rotating ellipse on a frictional surface as it
progressed in the "x" direction.

I pretended there was a lightbulb at the centroid of this rotating
ellipse that you capture on film using a very long exposure time.
That describes a series of cosine functions bounded by -pi/2 to pi/2.

Mariss