Imagine you are attempting to obtain a lagrangian model of a device with two inputs [u1, u2] and three outputs [O1, O2, x].

After some of lagrangian work, you find the following three unsimplified equations:

E1 = -u1+ Kb r^2 (O1[t] - O2[t]) + Kb r (1/2 r (O1[t] - O2[t]) -        Cos[alpha]x[t]) + b1 O1'[t] + I1 O1''[t] == 0  E2 = -u2 - Kb r^2 (O1[t] - O2[t]) - Kb r (1/2 r (O1[t] - O2[t]) -        Cos[alpha]x[t]) + b2 O2'[t] + I2 O''[t] == 0  E3 = Ks x[t] - 2 Kb Cos[alpha] (1/2 r (O1[t] - O2[t]) - Cos[alpha] x[t]) +        bs x'[t] + m x''[t] == 0  Kb, r, B1, I1, Ks, B2, I2, and m are known constants. alpha is a nonlinear element, which, if needed, may be linearized around 30 degrees. 

Regrerttably, probably due to misunderstanding the syntax, I cannot successfully apply LaplaceTransform on any of the three – but it is probably totally my fault, I’m very new to Mathematica.

What would you do next to isolate the systems transfer functions? Is there a way