Monday, May 30, 2016

Finally, Some Proof!

Dear Friend,

As Gabriel Kron wrote in his work on Generalized Machine Theory, there are similarities between the ElectroMagnetic(EM)/Mech. and other sciences and these similarities are not a coincidence nor do they mean that the concepts are fundamental to these sciences. In fact there are concepts that appear in all the sciences and are fundemental to all aspects of matter and fields of all sorts. One such concept is the idea of organizing any functioning system into inductive, capacitive and resistive elements. (For more on this, I refer you to my blog post: http://relmachine.blogspot.com/2011/02/would-kron-recognize-in-concepts-behind.html)

While the idea of an inductor may have been most clearly defined in EM systems, I propose that it is a fundamental property of Spacetime (as Einstein defined it). I propose that the gyroscope is an inductor-like device, with an impedance too. It can be shown that according to Einstein's Special Theory of Relativity, an object travelling at near-light-speeds traverses a shorter path in Spacetime than one at rest. I propose that in fact Mother Nature is the Ultimate Karma accountant and so even for speeds not approaching light speed this theory is true. I propose that a spinning wheel is the most elegant proof of this. The rim of the wheel has a larger linear speed than the center (which, technically is a singularity with zero linear speed) and that difference operates by Relativistic principles to produce a phase-difference in the energy distribution across the spinning wheel, and that is the source of the gyroscope's peculiar behavior. I further propose that Magnetism and all inductive phenomena have their roots in this specific theory. (For proof of the relativistic path difference between objects travelling at different speeds and more information on my thoughts on the subject you can refer to my blog post:
http://relmachine.blogspot.com/2009/05/spin-angular-momentum-and-worldlines.html
and also
http://relmachine.blogspot.com/2011/09/on-gravitomagnetism-and-compound.html)

Professor P. and I propose that the exact behavior of the gyroscope can be modeled as a nonlinear oscillator of the Van Der Pol type, while the fundamental modes can be analysed using linear state space techniques. We propose that the gyroscope really has two modes of oscillation only one of which is being exploited commercially today.
(For proof on the analysis of the modes of oscillation of a gyroscope, please refer to my blog posts: http://relmachine.blogspot.com/2015/04/analysis-of-analogous-networks-page-1.html
and also
http://relmachine.blogspot.com/2015/07/complete-characterization-of-gyroscopic.html )


I propose that the second mode is harder to invoke, but when activated, it is equivalent to the second mode of the electrical inductor, which is invoked when the inductor is coupled to a capacitor and resonated with a forcing function of the appropriate frequency. (Please note that although traditionally, Electrical engineers do not see the inductor as having two modes, I propose that its behavior w.r.t. DC current is a manifestation of its first mode and its behavior w.r.t. to an AC current is its second mode.

I propose that when commercially developed, the gyroscopic oscillator (G.O.) is capable of producing motion of a hitherto unseen kind - Large velocities without acceleration (i.e. inertial motion, unlike today's conventional wisdom which holds that an engine that produces velocity will concommitantly produce acceleration). This new kind of G.O. engine also has other peculiar properties dervied by analogy to EM inductors, such as ability to minimize friction, ability to behave in ways that violate Newton's Laws but obey the Lorentz Transform (i.e that it is Relativistic). Such engines which have much higher energy efficiency and also the ability to avoid collisions through precessive reaction to all collision-causing encounters.

Here is the summary of my proof:

1. Picture & Initial Video: You might want to first take a clear look at the picture of the basic prototype I am testing now. It is imaginatively titled "prototype august 2015".

First example: showing you that for a 'DC' torque, i.e. a torque that is not varying in its direction or amplitude, a smooth precession is produced.

2. "Sinusoidal Torque Right Frequency" video: Here I apply several sets of 6 cycles of torques each. The torque waves are analogous to AC current in that they vary sinusoidally, increasing from 0 to a maximum to zero and then reversing their direction for the rest of the cycle. This happens 6 times per cycle.

I can tell you that the friction on the lazy susan at the base of the rims has variable friction (what with me being a very delicate operator and all, and having bent it a bit over the months), so there is variable damping which muddles the picture....

But watch the video: It is 20 seconds of beauty - The beast is caught at the smoothest portion of the lazy susan, with even damping, and you can see that the gyro executes continuous circles! I can also tell you that continuous circles are only possible for this specific time period of the torques and will happen for any maximum amplitude torque at this specific frequency (within reasonable limites).

3. "Sinusoidal Torque - Wrong Frequency" video:  Any other frequency of the torque will fail to consistently produce full circles and will instead produce behavior similar to that shown in this video. I can prove to you that the power input to the gyro is the exact same as that of the previous video. The gyro just doesn't like the frequency. That is exactly how an inductor behaves - Right frequency - Open Sesame! Wrong frequency - Sorry, Wrong Answer.

I challenge anyone to prove me wrong by building a model that can produce smooth rotations of the gyro under arbitrary-frequency "AC torque" conditions! It is not possible! For DC torque, yes, you can produce smooth rotations of any frequency by adjusting the magnitude of the torque. But NOT AC torque.

I have found other peculiar things about gyroscopic behavior all of which are documented on my blog (http://relmachine.blogspot.com), but this has probably already taken too much of your time.

Thank You
Ravi


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