I need to know where you want to end up. I'd recommend letting some of your new LHS variables be equal to trig functions, like in the other thread.
I still need help to convert another system to that form, but this one has four input (u1 ... u4). m1, m2 and m3 are scalar. The dynamic system is:
xddot = u1
yddot = (m1/m2)*tan(psi)*u1
zddot = (-m1/m3)*tan(theta)*sec(psi)*u1
phiddot = u2
thetaddot = u3
psiddot = u4
Following Ackbeet's method in my other thread, and got like this pattern:
y1ddot = v1
y2ddot= v4
y3ddot = v3
y4ddot = v2
y5ddot = (m1/m2)y2v1
y6ddot = (-m1/m3)(1/sin(psi)) y2y3v1
May be the final solution can be simplify to be more close to the new form pattern, because in my calculation still has like sin(psi) in y6ddot. I want to check it with Ackbeet's calculation.
Thank you very much.