I've just started studying the motion of a rigid heavy (i.e. with gravity) spinning top using Euler's angles. It mostly makes sense, but there's one point in my notes where we've derived the equations of motion using Euler-Lagrange and one of them is (theta, phi are the usual Euler angles)
But P, I_1, I_3 and w_3 are independent constants so when theta gets really small (or close to pi) this is going to blow up. It obviously shouldn't since it's modelling a real object which can't spin infinitely fast, so why doesn't it?