Derivation of EoM for two interconnected rigid bodies

I set a small project for myself to design a controller for a rocket, which moves a mass around to shift the center of mass, in order to steer a rocket.

The picture shows a simplified model of a rocket plus a movable mass. , shown is a rod for the rocket, and a mass for the controller. there is a fixed thrust at the back of the rocket. (which I may change into a control parameter later in the project)

What do I need to know in order to go about writing down the equations of motion for this system? Do I need to know some more hardcore angular momentum (tensor of inertia, precession), or is basic fixed axis angular momentum enough? are there any chapters of textbooks that come to mind that contain the necessary topics I need to put this all in state space so I can design the controller? Any books that are just about deriving physical models of things in general?

Thanks

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jedishrfu
Mentor
I found this article on rocket engines (see page 4 and beyond) This describes a rocket that consumes its fuel and gets lighter but it might give you some insight into your problem.

https://ocw.mit.edu/courses/aeronau...fall-2009/lecture-notes/MIT16_07F09_Lec14.pdf

and here's a wikipedia article on thrust vectoring showing the center of mass and the torque that occurs:

https://en.wikipedia.org/wiki/Thrust_vectoring

Some references I saw said its best to keep the center of mass high on a rocket for stability so maybe shifting the center of mass around isn't a good idea as the rocket may flip. They tend to use fins to steer.