Re: [CAD_CAM_EDM_DRO] Math for constant speed ellipse

Hi Todd

Yes having looked at that I see it only works in the trivial case
of a=b. I had pulled out a Schaums for constant path speed
elliptical motion but it was in fact constant radial angular
velocity. They have misprints sometimes!

Constant dS/dt looks a little more busy.

So I duplicated and understand your diff equation.
Being non-linear I could only guess particular solutions.
I did not discover one, but I think f(t) is some cos^2 thing.
Or it might not be closed form soluble and have to be expressed
as an infinite series.

I will take a look at a parametric polar form to see if that gives any
insight.
I think that would be something like

r= 1/(1-ecos(f(t)))
theta=f(t)
where e is a constant between 0 and 1.

The only other thing I know is to try and conformally map it
(z-transform) it to solve in a potentially simple coordinate
system, than transform it back. I haven't done that stuff
in a long while though. You would need to map an ellipse
into a line or something.

Oh well when people find closed-form general solutions to non-linear
D.E. s they get it named after them right?

I can see it now- a Fleming function of the second kind.....

This may be one for numerical methods. I am just
not seeing anything symbolically simple. I did an internet search
and only saw Keplerian stuff (equal swept area).

As mentioned most any controller can do a polygon approximation
but I can see where a closed form might be useful in a CAM
program.

Les

Leslie Watts
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