How Do You Verify Equations for a Balancing Robot?

[auto]

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>

 

[auto]

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?