How to stabilize the aircraft flight after dropping boosters? I want to make aircraft model with boosters, but i don't know how to stabilize it. Аfter dropping the boosters, the center of mass of the aircraft will change, and I would also like to know whether it is necessary to stabilize it at all? Also during the flight on its own engine with fuel consumption, its mass will also change, whether in this case it is necessary to stabilize it? I need methods/ways or sources of info about it (maybe books, articles). Thanks for your attention.
The most important aspect is the vertical distance between the booster's thrust vector and the center of gravity. Once the booster stops working or is dropped, a pitch trim change will be needed to compensate for the upset in the pitching moment balance.

Next, the horizontal distance between the boosters and the center of gravity will tell you how much the pitching moment is changed upon dropping the boosters.

If control authority is sufficient to trim all those pitching moment changes, stabilization should not be much of an issue, especially if a sufficiently sized tail gives sufficient pitch damping.