More Old Hat

369(1): Complete Analytical Mechanics of the Gyroscope

January 27, 2017

The geometry is defined in Figure(1), and in general the gyroscope’s point is allowed to move with respect to the centre of the earth. So the point can move up or down. The analytical problem reduces to the simultaneous solution of four differential equations, (17) to (19) and (32). The first three are the same as in UFT368, for the pure rotational motion of the gyro. They are supplemented by Eq. (32) for the motion of R, where R is the distance between the point of the gyro and the centre of the Earth. Eq. (32) is the necessary link between the rotational and translation motions of the gyro. In the replicated Laithwaite experiment the point of the gyro (the common origins of (1, 2, 3) and (X, Y, Z)) is held at the height of Laithwaite’s arm.”

This is also not new.Mathematicians allow the vertical position of a spinning top to move when they need to study the effects of vibration. This does in fact lead to some fascinating new and anomalous phenomena, such as the appearance of subtle Hannay-angle effects. However, it cannot predict anti-gravitiional forces because a) the equations are still all predicated on Newton’s third law and b) all of the forces involved are still couples. The only hope of predicting anti-gravitational effects is to analyse the spinning-top using general relativity. That has already been done. Antigravitational levitation then becomes possible. Physicists have shown that the magnitude of the force developed is proportional to 1/c^2. It has been estimated that one would have to circulate (within a torus)  molten osmium at over Mach100000 in order to obtain an adequate force. And from what would one make the torus? Keep out of physics, Ron.

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