The idea he (and I) had was to counter the backwards thrust of the weapon recoil with forward thrust from the mech's thrusters (that is a lot of repetition of the word "thrust", and I apologise); the trick is figuring out how much backwards thrust the weapon generates so that he can adjust the thruster output accordingly. He's smart enough and has enough experience with mechs and weapons systems that he should be able to figure it out; I, on the other hand, have no idea how to go about this. The best I can come up with is that he could measure how many feet back the machine is pushed when the weapon is discharged and use ~MATHMAGIC~ to convert that into...some measurement of force/energy, but I'm not sure how accurate that would be or what sort of mathematical formula he would use. The scene wouldn't call for me going into explicit detail about the adjustments, but he would need to explain what factors he took into consideration and what role they played in his calculations.
I've Googled "calculating for weapon recoil compensation" and "recoil force correction", but these produce write-ups for patents or articles on nuclear physics; the former touch on what I'm looking for, but don't really describe how the force of the recoil is measured and then compensated for.
Can anyone help me, or do any of you have a better idea of how my character might solve this problem? Even additional suggestions for Google search terms would be appreciated.