Hi RMT
I was just lightly reading over that link you provided on the gyroscope. Since I have never been introduced to the cross product that you are talking about. So that caught my eye. I lightly looked through what a cross product is. It does seem like a rather complex way to describe an orthogonal torque. But it describes it without comprehension of just how or where that orthogonal torque came from.
So, I could address all of your points individually. But, let's cut to the chase. I'm sure you must be very curious by now.
Now you are just being cocky. Show me your math, sir. And properly define the 3 intertial reference frames you are talking about. Show me....don't give me "word salad".
Word Salad = Visualization. I have to give you the visualization first. It's just the way I comprehend how the physics behind a gyroscope works. I built this gyrodrive that I previously talked about 27 years ago. Actually there were three devices I built that showed promise of being developed into something that could get off the ground. I was out of work at the time for about six months. So I built lots and lots of mechanical devices to explore firsthand some of the ideas that were floating around at the time. Towards the end of those six months I started to explore the gyroscope. It must have been a dozen different configurations that I investigated.
It was seven years later that an idea came to mind about the gyro drive that was very intriguing to me. I wondered if mother nature had found a way to rectify centripetal acceleration in the gyroscope? Now this was strictly an armchair physics investigation. So I started my inquisition all on paper. The formula I used was Mass times Velocity squared divided by the Radius. I was interested to see if somehow the centripetal acceleration on one side of the spinning mass was being cancelled out.
So let's define the three inertial reference frames that I used to address the problem. I used the term "Radius of Curvature" to identify the individual inertial reference frames. I'm mainly interested in the inertial reference frames that would pertain to the spinning mass. The first inertial reference frame I chose was the base frame that the earth rotates in. It seems to be euclidian locally. But the radius of curvature to the spinning mass is around 8000 miles. The next inertial reference frame I chose was that of the spinning mass. The actual radius of the gyro would probably be around an inch. So the inertial reference frame for the spinning mass has a radius of curvature of one inch. And the third inertial reference frame would be the radius of the applied torque to the spinning mass. Let's pick a radius of three feet as the radius of curvature for the third inertial reference frame.
The way I approached the problem was to look at the velocity of the rotating mass relative to the first inertial reference frame. When the torque from the third inertial reference frame is applied to the spinning mass, there appears to be a velocity differential between one side of the spinning mass as opposed to the other side of the spinning mass relative to the first inertial frame. It actually looked like I was adding force vectors on one side and subtracting force vectors on the other side of the spinning mass. Can you legally do that? I don't know. But since it was an armchair physics venture, let's just see where it goes.
It went well. By combining torque vectors this way it appeared that I had mathematically modelled something that actually exists in the real world. So what I am saying is that there appears to be a centripetal force differential that appears orthogonally across the spinning mass when an outside torque is applied to the spinning mass as a whole. Ok, but that unbalanced centripetal acceleration acts like a torque too. So when it pushes the spinning mass, an additional orthogonal unbalanced centripetal force develops across the spinning mass in the direction that opposes the initially applied torque. That must be why the spinning mass seems to have more inertia. It's like a closed loop force. The initial input torque feeds back to cancel itself. Thus creating the effect of more mass or inertia.
M(V+v)^2/R - M(V-v)^2/R = X
M is calculated mass for each side of the spinning mass
V is the velocity of the applied torque
v is the rotational velocity of the spinning mass
R is the radius of the spinning mass
X is the resultant orthogonal torque
I wanted to post a drawing. But I can't access the site I use to store images. So I'll describe it. It's a drawing of the cross section of a current carrying wire. There is a circular magnetic field around the wire. This circular magnetic field is pictured within a much larger more uniform magnetic field where the lines of force all move in the same direction. This wire will move orthogonally across the larger uniform magnetic field because it is taught that the lines of force on one side of the wire will cancel out with the lines of force in the larger uniform magnetic field. I see a direct analogy between the behavior of magnetic lines of force and the way I described the behavior of the gyroscope or spinning mass.
I think mother nature uses this concept over and over throughout many portions of our reality. I went on to explore a little further just how the spinning mass would behave if the applied torque were in the same plane as the spinning mass. That was a very interesting mathematical venture. I would almost swear I was looking at the orbital dynamics of the electron. When I solved the equation for zero, I got two energy states. Doesn't the hydrogen atom have two energy states? Then I put it down, untill just recently. I have to ask the question: does time change direction with each orthogonal directional change of torque in the spinning mass? If the answer to that question is yes, then I am sitting on a unified field theory.
So I'm curious to see what you think about this, since it is very rare for me to actually find anyone interested in this kind of stuff.
Off I go, I got a motherload of stuff I want to get done today.