Heh, I am taking a course in machine dynamics starting tuesday. I could probably be a lot more help AFTER that course.
Lets see, symbols... Forgive me if I am stating the obvious to you, I'm not sure where you are at:
I'm sure you got theta and phi Kevin, both being angles.
dx/dt is the change in x in terms of t. The derivative of x with respect to t is dx/dt, which is also the velocity, providing x is the position.
If you take the derivative of the velocity, or the 2nd derivative of the position, you get acceleration. (d^2x/dt^2)
The Ohm sign there is confusing. The capital omega (the one we know as the ohm sign, for resistance) is angular velocity. The lower case omega is the curvy w. For some reason they aren't consistant with their usage, I'm not sure why.
Alpha is the angular acceleration.
This should be all covered in my course in machine dynamics, as I said. Unfortunately I don't know a lot about it yet.