I am trying to develop a little simulation (for the sake of learning a little bit about physics) involving a circle (mass m, radius r, regular density) and two forces f1, f2 that can be applied on any two points within the circle.
I have read that when a force doesn't go through the center of mass, then you have to split it up into two components, one parallel to the offset and one perpendicular to it. The parallel part of that force obviously now goes through the center of mass and thus "a=F/m" applies whereas the perpendicular force applies a torque, allowing me to use "alpha = torque/moment of inertia".
In my tests, this has worked perfectly, for as long as only one force acts on the body at a time.
However how (if at all) do I need to resolve multiple forces that influence the same body? At first I thought I can simply resolve each force in the pattern I described above and thus I calculated the sum of the linear forces on the CoM as well as the sum of the torque components. However this doesn't work for a number of examples, such as one where f1 and f2 act on either "side" of the circle in the same direction and both have the same length. For each individual force, there is no parallel component and thus no force is acted on the body. The sum of the torque is 0 as well, thus the body is not accelerated at all. However from playing KSP I realize that the net force applied on the body should be f1+f2.
This problem should have been solved numerous times, however I am unable to find a proper numerical solution (or don't use the right search terms). Can you guys help me out?