Suppose I have a physics simulation with a single body with three degrees of freedom (two axis and rotation). I have two impulses of equal magnitude in opposite directions. When applying these impulses in the same location, the body should not move in any way, the same if I apply them in spots that aligned in the same direction as the impulses. If I apply them outside of this axis, the object would gain momentum of some sort.
In some situations there would be a balance, in others a combination.
What is the right way of calculating the actual gain in momentum for the object? Calculating one impulse after the other would not (by what logic I use) create the right solution, as both impulses might add momentum in the same direction even if their torques might cancel one-another out.