How does a disk roll down an incline?

[Gogsey]

A uniform disk of mass m and radius R rolls without slipping down a ramp inclined at angle q to the horizontal.
Using the angle f through which it turns as a generalised coordinate, write the lagrangian, and then the Hamiltonian.
Write out and solve Hamilton’s equations of motion.

Ok, so I'm not really sure what to do here at all. Is ther 2 parts to the kinetic enerdy of the disk, one due to the disk spinning, and the other due to moving down the incline?

 

[Gogsey]

So I have my Lagrangian as:

L = (m(a phidot)^2)/2 + mga Phi sin(theta)

I did use a an example to start me off so I'm not sure what a is. Is a just the radius, which would be R for this example?

Also, whta is the definition of the Hamiltonian? Is it just the total energy T + U?

Lastly, what is Hamilton's equation of motion? Is it just H = pdot q - L?