367(4): Gyroscope Theory and Counter Gravitation

This note sets up the well known gyroscope equations and derives the gyroscope condition of classical dynamics, Eq. (26). The two reference frames (lab frame and moving frame) are related by a transformation matrix of Euler angles as is well known. In general the problem is exceedingly intricate, even on the classical level. It is shown that for direct counter gravitation (a positive force in the Z axis countering the negative force of the earth’s gravitation), the condition (27) must apply. So there cannot be direct counter gravitation in classical dynamics and the gyroscope does not lift off the ground. In ECE2 fluid dynamics however, direct counter gravitation can be described by solving Eqs. (28) and (29). So these equations can describe the Laithwaite and Shipov effects, assuming that they are repeatable and reproducible. There is often so much controversy over experimental reproducibility and repeatbility that I decided to go ahead as theoretician by assuming that the experimental results are true. Often, the controversy goes on for a hundred years or more. Note carefully that a Nobel Prize has been awarded for the Higgs boson, the data on which have not been repeated in another laboratory because of the astronomical expense. The LAithwaite experiment is simple, and Eqs. (28) and (29) are basically simple, so the conditions under which Laithwaite carried out his expriment must be used in Eqs. (28) and (29). In his experiment, r is the radius of his rotating wheel, and a lateral force F is applied to the rim of the wheel to make it spin. He holds the wheel in the axis perpendicular to the plane of the wheel. Denote this as the Y axis, the counter gravitational force appears to be in the Z axis.


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