Hamiltonian Method: Getting Final Equation of Motion

[oldspice1212]

Hey, I was hoping someone could clear this up for me. When using this method, how do you get the final equation of motion, that's where I am confused.

So I know I start off using Lagrangian (T - U) -> momentum (partial L/ partial q dot) -> Hamiltonian T+U, and then using the hamiltonian equation's of motion, we find the equations ( I can do this part). This is just a quick summary of the procedure. But, for some examples, they are taking time derivatives at the end for some equations, and finding the equation of motion. I don't understand why and where they come from?
Could someone please explain, thanks.

 

[jedishrfu]

This may explain it better than a post here:

http://www.people.fas.harvard.edu/~djmorin/chap15.pdf