a thought

I just spent an hour and a half replying to your post. I was almost done. With explanations about the way I solved the real math behind the gyro. My browser mysteriously closed on me. The whole reply was gone. I don't have another hour and a half to redo the reply today. Darn! It will have to wait till either tomorrow or the weekend. It's like I'm allowed to know the secrets behind a unified field theory, but I'm not going to be permitted to tell anybody. I will be back....

OK. I understand. No big rush or anything.

But maybe in the interim you could answer a simple question for me? Would you agree that the mathematics of the vector cross product "works" to describe the reality of this physical situation?

Thanks,
RMT
 
RMT

But maybe in the interim you could answer a simple question for me? Would you agree that the mathematics of the vector cross product "works" to describe the reality of this physical situation?

I need to see the original visualization in order to make any sense out of it. Since I found another path altogether, I might be biased in favor of my solution. But you know math by itself isn't science. I really do need to understand what went on in the mind of the author of the equations to make that kind of evaluation. I'll get some time in the morning to present my case.
 
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.
 
"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."

you have a big head start on me. in 1981, you were figuring out the gyroscope, i was busy being born. /ttiforum/images/graemlins/smile.gif
 
Einstein,

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.

This would tend to tell me that you do not have a good understanding of vectors and how they combine with one another. Have you had a class in vector statics, or even better vector dynamics? Recall that a vector has magnitude and direction. Force is a vector, and it is not only important what the magnitude of a force is, but it is also important in what direction that force is pointed. The vector cross product is a required way of doing mathematical business for how any two vectors are added together. I suggest it is something you should spend more time learning about, to see why the vector cross product reflects the reality of physics.

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.

That may be, but I do not have to read your word salad to know if your modeling equations are accurate. I can deal with the equations first, and then if you want to have a discussion of how you perceive the physical situation, we can do that later....after we ensure your equations accurately describe physical reality. That's just how I roll as a teacher.


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

There are a lot of questions I have for you about this equation and definitions.

1) Is this a vector equation? Are we to assume V, R, and thus X are all 3-D vectors? If so, are you aware of how you must perform vector math operations when you multiply or divide vectors?

2) Will this model account for differing mass distributions of the gyro rotor across its radius? This is the purpose of the real gyro models using Moment Of Inertia (I), rather than Mass (M)... The link I provided you derived the physical gyro relations using (I), which is a tensor, rather than (M) which is a scalar.

3)Are you aware that your units do not match on each side of your equation? Performing a dimensional analysis of either term on the left side of your equation yields fundamental units of:

[Mass]*[Length]/[Time^2]

But you define the left side (X) as a torque, which has units of:

[Mass]*[Length^2]/[Time^2]

4) Can you therefore understand that your equation is subtracting energy terms on the left hand side, but expecting them to equal a torque on the right hand side, and that this is therefore a fundamental error?

5) Have you tried to model these equations in MS Excel to produce tables of numbers that you believe can predict an actual calibrated gyro?

I think that is enough for now. Based on past discussions I have had with you, I have a feeling you will not answer my questions but instead complain about my approach of not paying attention to your words. But I am an engineer...and that makes me "equation man"... /ttiforum/images/graemlins/smile.gif I want to point out the basic problems in your equations to help you fix them. And I want to know if you understand vectors and how they represent physical reality. This is really important because it could result in a bigger "a ha" for you once you come to understand the power of vector and tensor mathematics.

RMT
 
RMT

That may be, but I do not have to read your word salad to know if your modeling equations are accurate. I can deal with the equations first, and then if you want to have a discussion of how you perceive the physical situation, we can do that later....after we ensure your equations accurately describe physical reality. That's just how I roll as a teacher.

Fair enough.

1) Is this a vector equation? Are we to assume V, R, and thus X are all 3-D vectors? If so, are you aware of how you must perform vector math operations when you multiply or divide vectors?

I do believe the equation falls into the clasification described as a quadratic equation. All the vectors are two dimensional. I believe my approach is probably a bit different than you are accustomed to seeing. In most situations where a torque is applied you see angular acceleration. But with a spinning mass there is an opposite feedback torque. The feedback torque produces a very interesting curve on a graph. But basically I'm looking at that stabilized constant precessional velocity with the three torques present. It does occur to me that I should probably be using the word speed instead of velocity since the torque is producing motion over a curved path.

2) Will this model account for differing mass distributions of the gyro rotor across its radius? This is the purpose of the real gyro models using Moment Of Inertia (I), rather than Mass (M)... The link I provided you derived the physical gyro relations using (I), which is a tensor, rather than (M) which is a scalar.

Yes, although I didn't mention it. I did use the word calculated to indicate there was some additional effort to determine the mass on each side of the spinning mass. I used a spinning mass ring and divided it up into one degreee increments. Then I just used one of the trig functions to calculate the amount of torque for each increment, then averaged them together for each side of the spinning mass. I do realize that calculus would probably have been a less time consuming approach. But not having a whole lot of experience applying calculus sort of had me at a disadvantage. But I remembered the way it was done before calculus. So I did it that way.

3)Are you aware that your units do not match on each side of your equation? Performing a dimensional analysis of either term on the left side of your equation yields fundamental units of:

[Mass]*[Length]/[Time^2]

But you define the left side (X) as a torque, which has units of:

[Mass]*[Length^2]/[Time^2]

No, I wasn't aware of that. Thanks for pointing it out. This information is in my memory and is 20 years old. So It appears that my memory is a bit rusty. I had notes, but my notes mainly covered the orbital dynamics of two torques in the same plane. So the way I have it set up: X should equal the resultant net centripetal acceleration.

4) Can you therefore understand that your equation is subtracting energy terms on the left hand side, but expecting them to equal a torque on the right hand side, and that this is therefore a fundamental error?

Yes, see my reply above.

5) Have you tried to model these equations in MS Excel to produce tables of numbers that you believe can predict an actual calibrated gyro?

The answer to that is no. But remember this was just an armchair physics endeavor. MS Excel didn't exist 20 years ago. And you know as well as I do that that the math can be made to fit with the fib factor. That was the day that my calculus teacher taught us how to make one equal two.

I think that is enough for now. Based on past discussions I have had with you, I have a feeling you will not answer my questions but instead complain about my approach of not paying attention to your words. But I am an engineer...and that makes me "equation man"... I want to point out the basic problems in your equations to help you fix them. And I want to know if you understand vectors and how they represent physical reality. This is really important because it could result in a bigger "a ha" for you once you come to understand the power of vector and tensor mathematics.

In this particular instance I'm willing to listen to you. Obviously I don't have the understanding of vectors that you do. I want to learn about time vectors. Especially orthogonal time vectors. It might be just an adventure in pure mathematical fantasy land. But I do have some actual experiments to try to see if they exist.
 
ruthless

i fell outta my seat when i read that!

Yeah, he does that to people. But me, having an open mind, have to let him have his say. The reason for that is sometimes I do experience an "ah ha" during a discussion with him. It's mainly when I put visualizations into words. I almost fell out of my seat when he called my visualizations "word salad". Reality through visualization beats mathematics hands down every single time.
 
I almost fell out of my seat when he called my visualizations "word salad". Reality through visualization beats mathematics hands down every single time.

But words are not visualizations, Einstein and you know that. I believe you also know that common language is an extremely imperfect manner for describing physical reality...which is precisely why the formal language called mathematics was invented. No matter how hard you try, you will never be able to express any visualizations you have in your head into english sentences that are free from inconsistencies. And so you are incorrect if you think your words=visualizations and that beats mathematics. It does not, as we shall see in my next post.

RMT
 
RMT

And so you are incorrect if you think your words=visualizations and that beats mathematics. It does not, as we shall see in my next post.

LOL.... Of course I just about fell out of my chair again............
 
No, I wasn't aware of that. Thanks for pointing it out. This information is in my memory and is 20 years old. So It appears that my memory is a bit rusty. I had notes, but my notes mainly covered the orbital dynamics of two torques in the same plane. So the way I have it set up: X should equal the resultant net centripetal acceleration.

You might want to try again. The units for acceleration (centripetal or otherwise) would come out as:

[Length]/[Time^2]

And you know as well as I do that that the math can be made to fit with the fib factor.

No offense, Einstein, but that description fits more of what you are doing than the actual physical analysis (which includes vectors and some calculus) that accurately describes how and why a gyro works.

In this particular instance I'm willing to listen to you. Obviously I don't have the understanding of vectors that you do. I want to learn about time vectors.

I am glad you are willing to listen. Because you could find what I am going to present to you now as a somewhat bitter pill to swallow. IMO I think you should endeavor to get a solid understanding of vectors (and why the vector cross product is necessary and accurate) before you begin examining time vectors.

What follows is a link to the exhaustive derivation of the gyro equations. As all good derivations do, this one begins with the most basic principles that are proven, namely Newton's "F=ma". It then goes through expansion of this basic principle in the domain of vectors and even shows how mass distributions (and yes, calculus applied to them) leads to the Moments and Products of Inertia (a 3x3 tensor). As noted on this web page, this derivation comes straight from a vector statics and dynamics book. Anyway here is the link. It is much more exhaustive and rigorous than the first link I gave you...but let me assure you, it accurately describes gyroscopic dynamics.

http://www.gyroscopes.org/math2.asp

The crux of this derivation comes to the 3 following scalar equations which describe the summation of all torques around the 3 principle axes of a gyro:

SMx = Ixq" - Iy(f')2cosqsinq + Izf'sinq(f'cosq + y')
SMy = Iy(f'q'cosq + f"sinq) - Izq'(f'cosq + y') + Ixf'q'cosq
SMz = Iz(- f'q'sinq + f"cosq + y") - Ixf'q'sinq + Iyf'q'sinq

{NOTE: The symbols that show up on the source page do not translate correctly here. I suggest you look at the equation in its native form on that page for a better representation.}

I would be more than happy to answer questions or help you through any tough spots you may encounter as you go through this, Einstein(and that goes for ruthless too, if he is so inclined to put in the time to study the derivation).

As an aside let me also tell you that coming to grips with vector math and the vector cross product will most definitely open a new world to you with respect to electric and magnetic fields and how they come into play in your "gravity wave" experiments. I had always thought, because you are certainly "good" with electronics, that you fully understood the physics of how the electric field and magnetic field relate to each other orthogonally. However, it appears I was mistaken. Because if you do not understand the vector cross product then it stands to reason you might not understand that the relationship between a current carrying wire, the magnetic field it generates, and the resulting force that is created is described by the following vector cross product:

F = i*L x B

Where:

i = current (rate of charge propagation)
L = the vector that describes the length of wire, in 3-space
B = the magnetic field vector
F = the resulting force vector that acts on the wire generated by the magnetic field

I hope you do not blow me off again and tell me how "my math" (or the accepted math) is wrong or does not describe reality. Because what I am trying to help you understand, Einstein, is that by coming to grips with the concept of vectors and vector mathematics, you will be in possession of a VERY POWERFUL tool to help you in your experiments... and as I always say, this will help you avoid going down the wrong path or formulating "visualizations" which are simply incorrect and in conflict with known physical laws.

RMT
 
A tutorial on vector cross product

Einstein,

I don't want you to get the idea that I disagree with you that "visualization" is a very good, and necessary thing. Only that visualization implies a diagram more than it implies what I call "word salad". In that spirit, let me give you a very good web page with a VISUAL (and interactive) tutorial on the vector cross product, and why it is necessary for multiplying two vectors.

http://physics.syr.edu/courses/java-suite/crosspro.html

Play with the Java applet and this should help you visualize how two vectors combine through multiplication via the cross product. If you like, I could also describe the difference between the vector cross product and the scalar "dot product". They both have very physical meanings.

RMT
 
RMT

I'm trying to comprehend the cross product concept. Now I can follow the description and see what the result is. But what I don't understand is why is the third orthogonal pseudovector being constructed? In my mind if I were to multiply two vectors together, I would get a two dimensional plane of force.
 
But what I don't understand is why is the third orthogonal pseudovector being constructed? In my mind if I were to multiply two vectors together, I would get a two dimensional plane of force.

First, it is not a "pseudovector". It is as real as any other vector. And here we have a perfect example of how visualization helps understand the math (as opposed to the other way around). /ttiforum/images/graemlins/smile.gif

We will use the concept of the torque vector to help you visualize why this 3rd orthogonal vector is real. As I am sure you know, a torque is represented as applying a force at some distance from a central (fixed) point. In the gyroscope link I gave you they formulate this as "r x F" where "r" is the distance from the central point to the point where the force (F) is applied. The best example to visualize this situation is when you turn a screw into wood. The reality of a screwdriver is that it applies a torque inside the screw head (a force at some distance from the center of the screw). Of course it is also easy to visualize what motion the torquing of the screwdriver induces...a rotation about that fixed point. But wait! It ALSO causes a displacement, doesn't it? Yes, indeed, when we torque a screw into wood it causes the screw to displace in a direction that is orthogonal to BOTH the "r" vector and the "F" vector. So the multiplication of the force (F) and its distance from the point of rotation (r) results in a motion that is at right angles to both of these vectors.

This is where the "right hand rule" comes into play that was described earlier. If you take your right hand and notice how your fingers curl. The direction your fingers curl would represent the crossing of the "r" vector into the "F" vector. As a result your thumb points in the direction that the screw will move. So if you point your right thumb down onto a screw that you are screwing into a piece of wood, you will notice that your fingers curl in the direction that you turn (torque) the screw.

This is the fundamental basis for why ALL vectors which are multiplied must use the cross product if you wish to preserve the magnitude of the multiplication AND also understand the resulting direction of the resulting vector that comes out of the multiplication.

Understand?

Here is another good link that will run you through an explanation of both the scalar (dot) product as well as the vector (cross) product mathematics.

http://physics.about.com/od/mathematics/a/VectorMath.htm

RMT
 
RMT

Thanks for the link. I'll get back to it later today. I have to attend a small gathering for the passing of a friend this afternoon.
 
"i fell outta my seat when i read that!"

i fell outta my seat because i envisioned ray in the hood, dressed like a pimp shouting, "thats how i roll!" extremely funny. /ttiforum/images/graemlins/smile.gif

"Reality through visualization beats mathematics hands down every single time."

yeah, i felt that way too. that is, until ray gave me a pop quiz from his aerospace engineering course. common sense isnt always reliable in it.
 
until ray gave me a pop quiz from his aerospace engineering course. common sense isnt always reliable in it.

This is a huge realization, ruthless. I commend you for that. Once you realize this you come to understand how important it is to use existing, known, and validated science to attempt to model any situation you are trying to understand, solve, or engineer. We always stand on the shoulders of the giants who came before us!

Believe me, what I do with airplanes is far from common sense. And each airplane is different, and non-linear is so many different ways! I would never think that I could "figure it all out" with visualizations in my mind. I am thankful for the people who came before me that quantified the science that I use to model complex vehicles. And it is ONLY BECAUSE I MODEL THEM MATHEMATICALLY that I can be confident in any of my designs and that they will work correctly.

This is also why I enjoy passing on the tool of engineering modeling to others (i.e. this is why I teach!). Because I have done such amazing things once I knew common sense does not always apply, and that I had to model something mathematically to understand it... that it made me want to share this enlightening knowledge with others who wish to study engineering.

I'm waiting to hear from you after you hear from the college you enrolled in. I hope it is good news!


RMT
 
after alot of thought, i realize that its almost impossible to model things mentally. your mind can alter variables that the world cannot. it was a hard realization for me to come to, but i did. i have no choice but to accept facts, and that is what you have proven to me, several facts.

"Believe me, what I do with airplanes is far from common sense."

as i have learned. and boy, do i have a long ways to go. i know its not out of reach though, and i am definitely up for the challenge.

"And it is ONLY BECAUSE I MODEL THEM MATHEMATICALLY that I can be confident in any of my designs and that they will work correctly."

i agree. because the mathematical model that you use has been proven to be reliable.

"This is also why I enjoy passing on the tool of engineering modeling to others (i.e. this is why I teach!). Because I have done such amazing things once I knew common sense does not always apply, and that I had to model something mathematically to understand it... that it made me want to share this enlightening knowledge with others who wish to study engineering."

common sense only took me so far. now its time for me to go to the next level, so to speak. my common sense and philosophical views can only take me so far without applicable knowledge to back it up.

"I'm waiting to hear from you after you hear from the college you enrolled in. I hope it is good news!"

ill know something on monday. i cant wait. im hoping to be able to tell you guys im enrolled. im crossing my fingers!
 
ruthless,

Did you play around with the Java applet for vector cross product? Hopefully you find it a good tool for visualizing what is going on with vectors in 3-D and how they multiply to create other vectors.

RMT
 
"Did you play around with the Java applet for vector cross product? Hopefully you find it a good tool for visualizing what is going on with vectors in 3-D and how they multiply to create other vectors."

i did. i am also reading the other link you gave, introduction to vector mathematics. this stuff is very complex to me. i am thinking that i am supposed to visualize a and b as a sphere and c as the axis. i dont know though, i need to get a better understanding of what im looking at. im fixing to read the rest of the article, maybe ill get a better understanding. i dont know though, the first page was totally foreign to me.

"Fx / F = cos theta and Fy / F = sin theta
which gives us

Fx = F cos theta and Fy = F sin theta"

could you please help me to understand what this means? im off to read the rest of the article, hope i "get it" before im done.
 
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