Hi everyone, I am currently working on a program which involves stabilizing a man wearing a jetpack at some arbitrary point along the vertical axis. This program is part of an experiment my faculty mentor gave me. Basically, what I am trying to do is have the Jetpack man stabilize at a point along the vertical axis by using control theory methods. I've already been able to animate my solution, yet for some reason the Jetpack man will not stabilize. I have a feeling this has to do with my equations of motion being wrong. I began with finding the Lagrangian for the energy of the system. What resulted is -9.8-u''[t] == f[t], where u''[t] is the acceleration of the Jetpack man. I then use a State Space model and subsequently LQR regulator gains to attempt to stabilize the Jetpack man at some point, say u[t] = 50. What happens is that he just falls indefinitely (beyond u[t]==0). I think that my kinetic energy for the jet pack is wrong. Can anyone help me derive this? I am also assuming that the jetpack has infinite amounts of fuel (not practical, I know, but that is not the point).