How Do You Verify Equations for a Balancing Robot?

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The discussion revolves around verifying the mechanical equations for a balancing robot, which consists of a body mounted on two wheels. The creator seeks confirmation on the correctness of the equations they have derived for both the body and the wheels. They mention that some initial equations were incorrect and are looking for feedback on any additional mistakes. Attached photos contain the equations in question for review. The focus is on ensuring the equations accurately represent the dynamics of the robot to maintain balance.
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Homework Statement


I am building a balancing robot like the one here:
http://www.geology.smu.edu/~dpa-www/robo/nbot/

It's basically a body mounted on two wheels and its purpose is to control the motors as to keep the wheels under the center of mass and therefore keep the body in an upward position.

I wrote the mechanical equations for the body and for the wheels separately, but I am not sure if they are correct. I need someone to check them, please.

Homework Equations


Are the equations in the attached photos correct?

The Attempt at a Solution


<see the attached photos>
 

Attachments

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  • DSCF7315.JPG
    DSCF7315.JPG
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Last edited:
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Scraping the J x Theta derived twice x ...
from the first two equations in the first pic.

Those were wrong.



Are there any other mistakes?
 
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