January 19, 2017
This note gives the complete set of equations for the motion of a gyroscope modelled as a symmetric top with one point fixed. These are Eqs. (27) to (29), and Eqs. (32) and (33) for the motion of Z(r), the height of the centre of mass of the gyro above its fixed point. In order for the gyro to lift off the ground, another force is needed in the positive Z(r) direction. Eqs. (32) and (33) can be solved for the motion of r using computer algebra.”
None of this is needed, and certainly not new. There is no force in the ‘positive Z(r) direction’, unless someone picks it up, and no internal force (especially not a fictitious one) can lift the top. That is Physics-101. Ah, but you are not a physicist are you? You are only a chemist armed, it seems, with just a couple of textbooks left over from your student days. If you really want the full gen on spinning-tops, we recommend, “Spinning Tops, a Course on Integrable Systems” by Michele Audin, CUP, 1996. But you will have to brush up your mathematics a good deal; you have never mentioned being familiar with Toda lattice or Lie algebra theory. Perhaps you should just retain this handy phrase, “spinning-tops cannot levitate, nor propel objects in outer space, and anybody who says that they can is a liar and a crackpot”.