Polynom of phi -> derivate to [mm/rad] and [mm/rad^2]

Hello everybody, I need your help!

I have a huge dataset for an ellipse.

Column 1 = degree from 0° -> 360°

Column 2 = radius (I define it as distance from the center) -> s [mm]

In the end I would like to plot the angular velocity [mm/rad] and the angular acceleration [mm/rad^2]. Therefor I used polyfit to get a function for the radius in dependency of degree -> s(°) with the unit [mm]

Now I would like to diff this function to get the angular velocity [mm/rad] and the angular acceleration [mm/rad^2].

The math looks like this:

s_dot = ds/dt = ds/dphi * dphi/dt = ds/dphi * omega

I have already tried it in several ways, but I’m not able to succeed.

Many thanks in advance!

Cheers

Christian

[Jan]

Usually teh term "velocity" has a relation to time. Do I understand correctly, that this is not so in your case?

[Christian]

Yes, you do understand that correctly! It is a normed velocity and acceleration with the unit [mm/rad] and [mm/rad^2].

You could also write it as velocity/omega or acceleration/omega^2

[David Goodmanson]

Hi Christian, by 'angular velocity' do you mean 'radial velocity'? It does involve ds, and it is in mm/rad.

[Christian]

Yes, you might be right! 'radial velocity' is what I mean. My ellipse is on a shaft which rotates. So the change of the radius causes a radial velocity for all points on the brink of the ellipse.

You could compare this problem to a camshaft where the velocity of the points on the brink of a cam looks like this:

[Christian]

I solved it!

s_strich=gradient(s, Shaft_deg).*(180/pi)

I used the diff function all the time, but the gradient function is what I was looking for. Simple as that :)