## Discussion of 367(8): Complete Theory of the Gyroscope

The theory of classical dynamics considered the Laithwaite configuration in all detail in Note 347(6), using the Lagrangian method as described by Marion and Thornton in their section 10.10. I used this as a course book when I was a professor of physics. It is theta = pi / 2 of that note. The spherical polar coordinates are equivalent to the Euler angles. Many thanks for this video! They are now all archived on www.archive.org via the blog. The problem was first worked out with great elegance by Lagrange in 1811 and 1815 in “Mecanique Analytique”. To describe the Laithwaite and Shipov experiments an extra torque is needed. That will be the subject of UFT368. Now I will write up my sections of UFT367. Horst might like to consider the fluid dynamic term in his section, using gnuplot. The motions of the earth and sun were considered in UFT119 (on equinoctial precession). The gyro is a three dimensional orbit of its centre of mass about its fixed point. Its equations are the three dimensional genealization of the 1689 Leibnitz equation of planar orbits, as shown in Note 367(8). These were worked out by Euler and Lagrange. Leibnitz hit on the right equation using an incorrect method. Newton did not devise these equations at all. I first studied them as a second year mathematics student in pure and applied mathematics at UCW. I think that GJE went through the same course three years later and Horst and Doug are completely familiar with the mathematics. My motivation in UFT367 is to work out the classical dynamics first to see if classical dynamics ever produces lift. It is obvious that it never does without an applied torque. Michael Jackson has already carried out the experiment with an applied torque. Gyroscope theory in classical dynamics is highly non trivial, and if people do not study the basic mathematics as in Marion and Thornton, they will not be able to understand the gyro at all. If they are great intuitive engineers like Trevithick or Brunel, they might be able to build a counter garvitational device. It is certainly possible as Laithwaite and Shipov have shown. I expect that the fluid dynamics term will be a small vacuum correction. Michael Jackson applied a very large mechanical torque.

Sent: 14/01/2017 18:01:07 GMT Standard Time

Subj: Re: Discussion of 367(8): Complete Theory of the GyroscopeMyron and Horst,

It’s not clear to me if your equations are considering the orientation of the axis of rotation relative to the direction of gravity.

Spinning Tops are oriented with the axis of rotation is parallel to gravity, while the Laithwaite experiments the axis of rotation is orthogonal to gravity.

Has the gravity frame orientation been included in your model? Does the rotation of the earth about its axis as well as around the sun also effect the fluid dynamics of the over all system? From the fluid model what also comes to mind is that when water drains from a bathtub it circulates in opposite directions depending on if it is in the northern or southern hemisphere.I don’t think this video was part of the set of links set but thought this one was good.

Gyroscopic Primer by Prof Eric Laithwaite Full Video https://youtu.be/OpCEJxO6V9g

SeanOn January 14, 2017 at 6:52:27 AM, emyrone@aol.com (emyrone) wrote:

Many thanks again, the gyroscope would be pulled upwards by its own spin, as we see in a spinning top, and this can be helped by a torque or force, or by spacetime itself in ECE2 fluid dynamics. So a gyro in a vehicle would tend to pull it up as you infer, but there is also the weight of the gyro to consider. So an extra torque is needed. Michael Jackson made such a device at home. The constants of motion and other information needed to simplify Eq. (25) are given in UFT270, with incisive graphics by Horst. For example the second term becomes L squared cos theta / (m squared r cubed), which is the centrifugal acceleration directed opposite to the pull of gravitation. The third term is also directed opposite to the force of gravitation, and is the Coriolis term. Laithwaite and Shipov use extra torques in the analysis.

To: EMyrone@aol.com

Sent: 14/01/2017 12:49:58 GMT Standard Time

Subj: Re: 367(8): Complete Theory of the GyroscopeAn important point is that it may not be able to generate lift itself but if it reduces the amount of energy that is required to produce a lift and propel an object forward then that in itself is technologically very important in reducing transport energy needs. Getting vehicles air borne and off traditional roads / rails would revolutionise transport and the need to maintain / improve the traditional transport infrastructure. If space-time energy could be used in transport this would revolutionise the sector.

These are very important developments and insights yet again by yourself and Horst.

Sent from my Samsung device

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