Angular Acceleration when accounting n-reference frames

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The discussion focuses on the equation for angular acceleration when three reference frames are considered and seeks to extend this to n-reference frames. Participants are exploring how to derive a generalized equation that incorporates multiple reference frames in angular motion. The conversation emphasizes the complexity of the mathematics involved in transitioning from three to n-reference frames. Clarifications on the underlying principles of angular acceleration and frame transformations are also discussed. Understanding these concepts is crucial for accurately modeling systems with multiple reference frames.
superfunnyshark
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Hello,

I understand the equation that describes the angular accelerator when 3 reference frames are involved is:

1707677790525.png


Now I would like to ask what is the resulting equation when accounting more than 3 reference frames, i.e. when n-reference frames are involved.

1707678336648.png


Thank you.
 
My idea is that I want to use immerse Whitetail Antlers in a fishtank to measure their volumetric displacement (the Boone and Crockett system is the current record measurement standard to place in a juxtaposition with) I would use some sight glass plumbed into the side of the tank to get the change in height so that I can multiply by the tank cross-section. Simple Idea. But... Is there a simple mechanical way to amplify the height in the sight glass to increase measurement precision...

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