Hi Arda,
These two equations are of the form
p' Jxx - r' Jxz = f(...) where ... = p,q,r,J,J,M,M (a bunch of known stuff)
-p' Jxz + r' Jzz = g(...) where ... = a bunch of other known stuff
in matrix form this is
[Jxx -Jxz; -Jxz Jzz]*[p'; r'] = [f; g];
where the semicolons produce a 2x2 matrix and two 2x1 column vectors. This is solved by left divide.
[p'; r'] = [Jxx -Jxz; -Jxz Jzz]\[f; g]
which works fine for calculation, or if you prefer you can use the tedious longhand version
p' = (Jzz*f + Jxz*g) / (Jxx*Jzz - Jxz^2)
r' = (Jxz*f + Jxx*g) / (Jxx*Jzz - Jxz^2)
