January 30, 2017
Many thanks again, and congratulations in turn! This rigorous solution shows that the spinning of the gyroscope cannot balance the force of gravitation without an extra upward force. The elliptic spiral is particularly interesting, the centre of mass follows this path as it is pulled downwards by the force of gravity. A balancing upward force modelled by m = m1 allows the gyro to float, so if held above the lab bench it would feel weightless. This is the observation by Laithwaite, who was perfectly right. This effect can be used for heavy engineering, for example to reduce drag in railway systems. That requires the skills of a practical engineer. All this shows the power and elegance of the Euler Lagrange equations.”
The spinning of the top (have you ever seen a real gyroscope) cannot indeed produce an upward force. Duh! But adding a contrived extra force proves nothing. Let us imagine that this ‘loony-force’ relieves Laithwaite of the effort required to lift the top. How does that change anything? The loony-force will still (unless it is truly magical) exert a reaction force on the ground, and so it is still not the wonderful antigravity force (one that does not obey Newton’s third law) which is always sought by the lunatic fringe. In fact, even the levitation effect predicted by general relativity (which we mentioned recently), would still obey the third law. We wonder whether your degrees are worth the paper that they are printed on. After all, teachers often simply mark, as correct, the incorrect information which they handed out in the first place! Is that what happened to you … and SS? Or did you both happen to miss the third-law lesson?