I was wondering if someone would share some insight into a bit of a conundrum I'm currently working on. This is a general physics question, nothing specific on Newton, but since I'm using Newton, I thought it would be appropriate to ask here.

I am trying to roll a cylinder by an exact amount of, let's say, 60 degrees. I am applying external forces to it which, in their configuration, produce a perfect longitudinal torque, thus rolling the cylinder on its longitudinal axis.

In ideal conditions, this would be fairly straight forward:

-Apply forces to initiate the roll

-At a half way point (30 degrees in this case) reverse the forces

-At zero axial omega, stop the forces. The body should be at exactly 60 degrees.

However - there are several factors I have to consider in my case:

-The body is losing mass - it is becoming lighter and thus has less moment of inertia with time

-The body has to contend with an angular damping coefficient which is decreasing with time.

This is due to the factors specific to my situation: It is a rocket, being launched through atmosphere. Cylinder is a rocket body, and it is losing mass as it burns fuel. Angular damping coefficient is the resistance to rotation in atmosphere, and it decreases as the atmosphere gets thinner.

With the factors above, it is apparent that if I reverse the forces at half way point, the roll will be stopped before I reach the goal of 60 degrees, since it requires less torque to stop a lighter body.

I need to calculate a point, during the roll, sometimes after 30-degree mark but before 60 degrees, where I can reverse the torque, to end up at exactly 60 degrees.

Any thoughts on this?