How to Derive the Simplified Form of Modified Euler Equations?

[Telemachus]

Homework Statement

Hi there. I'm not sure if this question corresponds to this subforum, but I think you must be more familiarized with it. The thing is I don't know how to get from:

$$M_x=(I_0-I)\dot\Psi^2\sin\theta\cos\theta+I_0\dot\Phi\dot\Psi\sin\theta$$

to:
$$\dot\Psi=\displaystyle\frac{I_0\dot\Phi}{2(I-I_0)\cos\theta} \left[1\pm \left( {1-\displaystyle\frac{4M_x(I-I_0)\cos\theta}{I_0^2\dot\Phi^2\sin\theta}}\right)^{1/2}\right]$$
I don't know how to get Phi from the first, but this is the simplification given on my book, but I don't know which intermediate steps to give.

Bye, and thanks.

 

[gneill]

Looks like a pretty straightforward application of the quadratic formula to find Psi-dot.

 

[Telemachus]

Right. Thanks.