367(8): Complete Theory of the Gyroscope

After some discussions with co author Horst Eckardt I produced this new and original theory of the gyroscope, or spinning top, giving the force equation (25) in terms of spherical polar coordinates. It shows very clearly that the force due to gravitation is counterbalanced by three dimensional centrifugal and Coriolis forces when the gyro is spun. Eq. (25) reduces to the Leibnitz equation of planar orbits under the conditions (26). So the gyro is a type of three dimensional orbit. The analysis of three dimensional orbits by Horst and myself in previous UFT papers can be used to see if there are constants of motion in Eq. (25). It could then be solved. Eq. (13) is always true so the gyro cannot lift itself off the ground without an extra force or torque, which may be mechanical or may come from ECE2 fluid dynamics. So I will now write up my part of UFT367, Sections 1 and 2 as usual, around the finished theory of Note 367(8). The use of spherical polar coordinates gives great insight into the motion of the gyro. I congratulate the group on an excellent discussion.


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