368(1): Complete Rotational Dynamics of the Classical Gyroscope

These are described in the attached note, the motion is the same as the spherical orbit motion graphed in UFT270, with some additional features.The equations of motion (15) to (17) can be integrated to give the trajectories beta(r), phi(r) and theta(r). The gyroscope is characterized by the relation between beta and phi in Eq. (20) and between theta and phi in Eq. (22). The lagrangian method is used as in UFT270 and its notes. As mentioned by Michael Jackson recently, this is the first complete solution of the classical gyroscope problem in about four hundred years. The same is true for the solution of spherical orbit motion in UFT270. Some of the very interesting graphics in UFT270 could be extended and developed for UFT367 and UFT368. The next stage is to introduce a lifting force as in the Braithwaite and Shipov experiments. Much of this theory became the basis for quantum mechanics, there is a photograph on the net of Heisenberg and Pauli looking intently at a simple gyroscope (spinning top). I think that they were both students of Sommerfeld.


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