JL*QL'' + BL*QL' + k(QL - Qm) = 0 Jm*Qm'' + Bm*Qm' - k(QL - Qm) = u This is the equation set I have for a motor with a load. QL'' means second derivative and QL' means first derivative. I need to be able to obtain the state space representation of this model where X = [QL;QL';Qm;Qm'] (This is of course a column array) I tried my best but couldn't obtain it. Started off with QL' = [-JL*QL'' - k(QL - Qm)]/BL But when I try to represent this, I don't have the QL'' term in my state variable array X, so couldn't proceed further. How am I supposed to approach this problem ?