I was thinking about gyroscopes to me, and it became apparent that I'm really not comfortable with why a gyroscope attached to a pivot, with its axis parallel to the ground, doesn't swing about the pivot like a pendulum. I remembered learning something to the effect that it has to do with the precession of the gyroscope, but I couldn't quite figure it out, so I got out my mechanics texbook (by Kleppner and Kolenkow), and read up on what they had to saw about gyroscopes. They do the standard derivation of the equation for the angular velocity of precession, but the derivation depends on the fact that the gyroscope is no longer in the transient state, and the gyroscope is already precessing with uniform angular velocity. My question, is how does a gyroscope start precessing in the first place? It seems like the gyroscope will initially start to fall, and somehow this motion will evolve into the precession of the gyroscope. This could make finding the general equation for the motion of a gyroscope significantly more difficult than the special case when the gyroscope is already precessing! Can anyone offer insight as to what is going on?