I am making a 2d user build spaceship game that allows the user to place thrusters where they would like. I've read a bunch of posts in a lot of places including stack exchange on how determine the lateral force and torque force.
My problem so far with the information that I have is that it seems to me that they all are assuming that the axis of rotation for torque will always be at the center of mass. Obviously a well designed thruster placement will have the rigid body rotate about its center of mass but some damage can ruin that and to be frank I want the user to be able to make not well designed ships just because it's fun.
My main question really is what terminology am I missing that allows me to find out the relationship between the center of thrust and the center of mass so that I can find the true rotation axis for torque.
Here is an example of a craft that won't rotate about its center of mass: