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

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Christian 2017-1-18

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编辑： Christian 2017-1-19

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

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Christian 2017-1-19

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: