Modeling pitch of a rocket

[makosz]

I am working on my senior design project and have exhausted all my resources. I need to make a mathematical model of a pitched rocket in order to create a PID controller using vector thrusting. I read that it can me modeled as a Mass-Damper-Spring system, with damping coefficient being related to the change of coefficient of the moment with respect to an angle of attack. While spring linear to the moment.

I tried to get a coefficient of the moment through simulating the rocket at different angles of attack but student edition of the software is limited to an extent that I don't get any good results. The project timeline is not long enough for us to learn OpenFoam. So how would I go about either simulating the rocket or analytically computing it? Please provide sources for further reading when possible.