Thread: Principal Axes of Inertia (a challenge)

Hi scientists.

I am a programmer and I've been asked to get the (Principal Axes of Inertia) given only the coordinates.

I've been searching for a formula for the Principal Axes of Inertia with a given values of (x,y) axes.

Example:
0,4
12,59
10,100
3,498

But I can't find anything related to my problem.

Is it possible to get Principal Axes of Inertia given only the coordinates?
Sorry, I don't have any idea. I'm asking for your help.
I'm not even sure if I posted on the right section.

Thanks in advance.

-
phirong

Originally Posted by phirong

Hi scientists.

I am a programmer and I've been asked to get the (Principal Axes of Inertia) given only the coordinates.

I've been searching for a formula for the Principal Axes of Inertia with a given values of (x,y) axes.

Example:
0,4
12,59
10,100
3,498

But I can't find anything related to my problem.

Is it possible to get Principal Axes of Inertia given only the coordinates?
Sorry, I don't have any idea. I'm asking for your help.
I'm not even sure if I posted on the right section.

Thanks in advance.

-
phirong

I have seen just about every crazy device on earth. But I have never heard that term before.

The word inertia actually did not mean movement. It might have been misunderstood, in its use by the Universal Scientists. And then later changed to fit some other scheme.
In other words if something is just sitting there, it is really not just sitting there. It is on a spinning planet, revolving around a sun. And only God knows what our solar system is doing. And or the Universe.



Today in physics it means either rest or straight line motion.

Axes means Axis. And can be the pin in a door hinge, or the imaginary line from the North to South Poles. That the planet revolves around.

From those two dimensional coordinates, I would have trouble deciphering what they want.

You could assume that the origin of the two coordinates given is zero. That could be the axis and the other two coordinates might give you the objects radius. From that you could assume some gravitational force. And then decide what you want because I have no clue. Ha-ha.

Sincerely,


William McCormick

phirong: Ignore William McC.

I'm sure someone here should know enough classical mechanics to help you out. I don't. However, if nobody steps up, I might be able to help if you explain what the given coordinates are supposed to represent.


William: This isn't some sort of new-fangled concept. Euler was talking about it in 1730. We knew you didn't know anything about modern physics, but now it's clear you just don't know anything about physics period.

Originally Posted by serpicojr

phirong: Ignore William McC.

I'm sure someone here should know enough classical mechanics to help you out. I don't. However, if nobody steps up, I might be able to help if you explain what the given coordinates are supposed to represent.


William: This isn't some sort of new-fangled concept. Euler was talking about it in 1730. We knew you didn't know anything about modern physics, but now it's clear you just don't know anything about physics period.

I do understand any force in the Universe. I openly admit I do not use modern terms, and I am proud of that. History shows that most of the older terms have changed many times over the last 100 years.

I only get in trouble when I try to communicate with modern terms. Because the terms are so useless by definition.

Sincerely,


William McCormick

A rose by any other name would smell as sweet. Take a minute, spend a little effort, try to learn what terms mean in terms of what you're used to. Dismissing something simply because it's couched in language with which you're not familiar is silly. It's all just... words, words, words!

Originally Posted by serpicojr

A rose by any other name would smell as sweet. Take a minute, spend a little effort, try to learn what terms mean in terms of what you're used to. Dismissing something simply because it's couched in language with which you're not familiar is silly. It's all just... words, words, words!

Almost any term that has stuck today. Whether it be new or old. Is the worst term possible. The terms of today are almost all backwards. Because the basic terms are backwards or misapplied.

I check the terms out, and then try to decipher what simple thing they are complicating. I have no other reason to figure them out. I can do anything I wish, I have no scientific limitations. I am just a little short of manpower.


Sincerely,


William McCormick

For how long will this lunatic have free reign? William, you reach new levels of delusion on a dayly basis. I don't have any pull to get you banned, but I can assure you that if I had been a moderator, I would certainly have requested such from the admins. You are severely damaging the credibility of this forum with your unchecked and frequent presenting of your personally derived "theories" as fact, despite many appeals for you to restrain yourself.

Originally Posted by KALSTER

For how long will this lunatic have free reign? William, you reach new levels of delusion on a dayly basis. I don't have any pull to get you banned, but I can assure you that if I had been a moderator, I would certainly have requested such from the admins. You are severely damaging the credibility of this forum with your unchecked and frequent presenting of your personally derived "theories" as fact, despite many appeals for you to restrain yourself.

Well, what is the simple solution to the problem posted?

What technical information that I posted did you disagree with?


Sincerely,


William McCormick

Originally Posted by KALSTER

For how long will this lunatic have free reign? William, you reach new levels of delusion on a dayly basis. I don't have any pull to get you banned, but I can assure you that if I had been a moderator, I would certainly have requested such from the admins. You are severely damaging the credibility of this forum with your unchecked and frequent presenting of your personally derived "theories" as fact, despite many appeals for you to restrain yourself.

I see no problem in Bill's daily delusional fixations. He is equally ignored by all as a relatively harmless imbecile, which unto itself provides great value and credibility to this forum by keeping him around to bleat that which is unfathomable gibberish.

He could be our pet monkey.

Originally Posted by (Q)

Originally Posted by KALSTER

For how long will this lunatic have free reign? William, you reach new levels of delusion on a dayly basis. I don't have any pull to get you banned, but I can assure you that if I had been a moderator, I would certainly have requested such from the admins. You are severely damaging the credibility of this forum with your unchecked and frequent presenting of your personally derived "theories" as fact, despite many appeals for you to restrain yourself.

I see no problem in Bill's daily delusional fixations. He is equally ignored by all as a relatively harmless imbecile, which unto itself provides great value and credibility to this forum by keeping him around to bleat that which is unfathomable gibberish.

He could be our pet monkey.

You couldn't afford the bananas.

I have found axes inertia, it was on Ebay.

http://www.Rockwelder.com/EastWood/spinningthing.wmv


Sincerely,


William McCormick

Originally Posted by (Q)

Originally Posted by KALSTER

For how long will this lunatic have free reign? William, you reach new levels of delusion on a dayly basis. I don't have any pull to get you banned, but I can assure you that if I had been a moderator, I would certainly have requested such from the admins. You are severely damaging the credibility of this forum with your unchecked and frequent presenting of your personally derived "theories" as fact, despite many appeals for you to restrain yourself.

I see no problem in Bill's daily delusional fixations. He is equally ignored by all as a relatively harmless imbecile, which unto itself provides great value and credibility to this forum by keeping him around to bleat that which is unfathomable gibberish.

He could be our pet monkey.

In all seriousness did you read the Wikepedia inertia definition. That is really out there.

http://en.wikipedia.org/wiki/Moment_of_inertia

That is sad. They missed the whole point of what takes place with a moving object. An object only likes to travel in a straight line.

If you increased the gravity on a satellite, that was in a stable orbit above a point on the surface of the earth, it would start to fall in towards the planet. And it would orbit the earth faster.

When an ice skater pulls her arms in. She expends energy, by pulling her arms in. She creates the effect of her arms being put under more gravity, like a satellite would react to more gravity.

Sincerely,


William McCormick

Originally Posted by William McCormick

http://en.wikipedia.org/wiki/Moment_of_inertia

That is sad. They missed the whole point of what takes place with a moving object. An object only likes to travel in a straight line.

If you increased the gravity on a satellite, that was in a stable orbit above a point on the surface of the earth, it would start to fall in towards the planet. And it would orbit the earth faster.

When an ice skater pulls her arms in. She expends energy, by pulling her arms in. She creates the effect of her arms being put under more gravity, like a satellite would react to more gravity.

And what do you think is wrong there? This is all about a rigid body and how it spins. The example of this ice skater is also correct, but it is no contradiction to what is explained there. Did you notice that the inertia of a rigid body (against change of rotational states) is dependent on the mass distribution (sum over m times r)? The angular momentum L=I*omega is conserved in this example (as it should), because the mass of the skater is redistributed. So, I (inertia) changes, and as a consequence omega (angular velocity) has to change as well.

If I remember well (classical mechanics lectures have been a long time ago), the Principle Axes of Inertia are something like a coordinate transformation of the inertia tensor of a rigid body to three main axes. In an experiment, you would notice these axes as the main rotation axes. It is all very easy for simple bodies (cylinders or spheres) but can be very complicated for arbitrary bodies. As you can break down any translatory movement in the three base coordinates of the 3D space, you can describe every rotation as a superposition of rotations around the principle axes. But I have forgotten how to actuelly calculate them. But WMcC's link should give you at least a hint. There are also other links that could help.

Originally Posted by phirong

I am a programmer and I've been asked to get the (Principal Axes of Inertia) given only the coordinates.

I've been searching for a formula for the Principal Axes of Inertia with a given values of (x,y) axes.

Example:
0,4
12,59
10,100
3,498

But I can't find anything related to my problem.

Is it possible to get Principal Axes of Inertia given only the coordinates?

Hi Phrong.

For a two-dimensional object I would guess that the main rotation axis (taking Dishmaster’s word for it that this is the same as the principal axis of rotation ) would be the axis perpendicular to the object and passing through the centre of mass.

If the area bounded by the given co-ordinates has uniform density, then the centre of mass coincides with the centroid, which is given by a simple formula: the centroid of the area bounded by the n points (x₁,y₁), (x₂,y₂), …, (x_n,y_n) is , where





By the way, Phrong, there’s another useful thing you can do around here. Click the following link: http://www.thescienceforum.com/ignor...am%20McCormick

Originally Posted by JaneBennet

By the way, Phrong, there’s another useful thing you can do around here. Click the following link: http://www.thescienceforum.com/ignor...am%20McCormick

Ah, very useful. Cheers!

This appy should help visualize tensor change in inertia for more complicated mass configurations.

http://demonstrations.wolfram.com/Pr...AxesOfInertia/

Originally Posted by Dishmaster

Originally Posted by William McCormick

http://en.wikipedia.org/wiki/Moment_of_inertia

That is sad. They missed the whole point of what takes place with a moving object. An object only likes to travel in a straight line.

If you increased the gravity on a satellite, that was in a stable orbit above a point on the surface of the earth, it would start to fall in towards the planet. And it would orbit the earth faster.

When an ice skater pulls her arms in. She expends energy, by pulling her arms in. She creates the effect of her arms being put under more gravity, like a satellite would react to more gravity.

And what do you think is wrong there? This is all about a rigid body and how it spins. The example of this ice skater is also correct, but it is no contradiction to what is explained there. Did you notice that the inertia of a rigid body (against change of rotational states) is dependent on the mass distribution (sum over m times r)? The angular momentum L=I*omega is conserved in this example (as it should), because the mass of the skater is redistributed. So, I (inertia) changes, and as a consequence omega (angular velocity) has to change as well.

If I remember well (classical mechanics lectures have been a long time ago), the Principle Axes of Inertia are something like a coordinate transformation of the inertia tensor of a rigid body to three main axes. In an experiment, you would notice these axes as the main rotation axes. It is all very easy for simple bodies (cylinders or spheres) but can be very complicated for arbitrary bodies. As you can break down any translatory movement in the three base coordinates of the 3D space, you can describe every rotation as a superposition of rotations around the principle axes. But I have forgotten how to actuelly calculate them. But WMcC's link should give you at least a hint. There are also other links that could help.

I have not gotten past inertia yet.

I also do not get angular velocity. The object is traveling in an arc.



It appears to me that you would have to change the center of gravity of the object being orbited, to maintain a more perfectly straight line or unchanging ARC like orbit.

Assuming that the object in orbit, or on a tether will not move, shake or vibrate the object in anyway. This creates the effect of more gravity. (Edited Less Gravity) Because the natural eye of the gravitational force would have to move in order for the object to maintain a straight path.

I am looking at this drawing from the point of view an orbiting satellite is nudged downwards, while it was in a stable orbit. It would create less gravity. Which is almost too obvious. Ha-ha.

Sincerely,


William McCormick

Originally Posted by William McCormick

I have not gotten past elimentri skewl yet.

Sincerely,


William McCormick

phirong: Okay, here's my stab. I'm assuming that the coordinates you're giving are the coordinates of point masses. The one thing missing is then the mass of each point. Given this info, you can calculate the moment of inertia tensor using this definition:

http://en.wikipedia.org/wiki/Moment_...a#Definition_2

Note that, since you're working in the plane, you'll have a 2x2 matrix. There are a couple of formulas given for the components. Personally, I think the second set of formulas (the ones without the Kronecker delta) would be most useful in your case.

Now this is a real, symmetric matrix. So it has two real eigenvectors. Use linear algebra to find them. (E.g., letting I be the matrix, calculate the characteristic polynomial det(t-I), find the roots a and b, and then solve the equations (a-I)v = 0 and (b-I)v = 0.)


William McC: You once again display that you have no idea what's going on. The question is not about one body revolving about another. It's about a single rigid system and its rotation. Words!

Originally Posted by serpicojr

phirong: Okay, here's my stab. I'm assuming that the coordinates you're giving are the coordinates of point masses. The one thing missing is then the mass of each point. Given this info, you can calculate the moment of inertia tensor using this definition:

http://en.wikipedia.org/wiki/Moment_...a#Definition_2

Note that, since you're working in the plane, you'll have a 2x2 matrix. There are a couple of formulas given for the components. Personally, I think the second set of formulas (the ones without the Kronecker delta) would be most useful in your case.

Now this is a real, symmetric matrix. So it has two real eigenvectors. Use linear algebra to find them. (E.g., letting I be the matrix, calculate the characteristic polynomial det(t-I), find the roots a and b, and then solve the equations (a-I)v = 0 and (b-I)v = 0.)


William McC: You once again display that you have no idea what's going on. The question is not about one body revolving about another. It's about a single rigid system and its rotation. Words!

What is the difference between one object or a tethered object? I do not see any.

When an ice skater pulls in here hands. She is creating a variable force of gravity or counter centrifuge action, in a short period of time. This creates the velocity because, she created the velocity.

Here hands follow that volute pattern. The harder she pulls, the more quickly the pattern is completed. The more revolutions are made in a shorter period of time.

The spinning singular object, in real life is almost never a single thickness odd shaped piece of metal.
Even when it is, it almost always has fasteners or other things attached to it. And we still have to put it up on a high speed balancing machine, and add or remove metal, and get it to stop vibrating.

But I like the idea of centering weird objects.

Sincerely,


William McCormick

Originally Posted by (Q)

Originally Posted by William McCormick

I have not gotten past elimentri skewl yet.

Sincerely,


William McCormick

You have shewn an inability to duplicate what was said.

Sincerely,


William McCormick

Originally Posted by William McCormick

What is the difference between one object or a tethered object? I do not see any.

First, the rotational inertia of a rigid system is fixed, while that of a nonrigid system may vary, as you yourself have discussed via the example of the figure skater. Second, you started talking about revolution, which is linear displacement, not rotation.

In any case, the guy asked a very specific computational question, and your discussion really had nothing to do with it.

Originally Posted by serpicojr

Originally Posted by William McCormick

What is the difference between one object or a tethered object? I do not see any.

First, the rotational inertia of a rigid system is fixed, while that of a nonrigid system may vary, as you yourself have discussed via the example of the figure skater. Second, you started talking about revolution, which is linear displacement, not rotation.

In any case, the guy asked a very specific computational question, and your discussion really had nothing to do with it.

I agree my discussion was about understanding what kind of computational thing he was looking for.

I was not trying to confuse anything. Believe me it seems more then confusing enough now.

Also I am still trying to figure out, what inertia is and was. I am trying to figure out what this angular velocity is as well. The ice skater although a singular object. Brought into play the conversation of a changing solid object.




Sincerely,


William McCormick

Originally Posted by serpicojr

Originally Posted by William McCormick

What is the difference between one object or a tethered object? I do not see any.

First, the rotational inertia of a rigid system is fixed, while that of a nonrigid system may vary, as you yourself have discussed via the example of the figure skater. Second, you started talking about revolution, which is linear displacement, not rotation.

In any case, the guy asked a very specific computational question, and your discussion really had nothing to do with it.

I read this again. I will admit I have a problem. It is with the words.

Often I hear inertia used as the stored energy in an object. And yet the original definition was that, inertia meant at rest, without reactive power. Inert.
I have used it over the years only because others have been using and referring to it as stored energy. I was wrong actually, but I was able to explain something to them.

Now I know times change, and words definitions change. However inertia may still have a problem. Because even its current definition really is that an object moving in a straight path, will display a want to stay in a straight path.

And although when proving perpetual motion this may come in handy.
In getting to the root of understanding of this rotating inertia axes or whatever it is, it is the wrong word.

It is actually a misuse, in my opinion. Because a rotating object is not moving. And it is not moving in a straight line. A rotating object is, spinning. It is doing anything but straight line movement. In fact it is not moving. It is turning. It is not changing position or posture.

Take a look at these definitions and the care and wording they use to avoid including spinning objects. Even in the motion definition.

So you can poke fun at me. But if you are honest you will see that the basis for all this stuff, that may be wonderful to use. Is to flawed and all to misunderstood to make use of it in life and death situations.





I hope you trust my motives. Ha-ha.





Sincerely,


William McCormick

Your standard dictionary is not the right place to look up the technical meanings of scientific terms. Surely you understand that common usage of words often differs from technical usage.

Originally Posted by serpicojr

Your standard dictionary is not the right place to look up the technical meanings of scientific terms. Surely you understand that common usage of words often differs from technical usage.

I have never argued that the definitions of words have undergone some wild changes. However, I am stating that if the scientific world chose inert, as the definition of the energy of a spinning object.
I believe they should shut down, go back and find out what science is. And how important it is. Language experts ought to do the same.

A scientist ought to know English, and English expert ought to know science. That is what destroyed real science.

If they meant inert, they should not have allowed the opposite definition to be used and created.

As an amateur scientist, I know I cannot put any of this nonsense into the realm of science. It belongs in comedy. We need a language again and science again and math again.

The good news is we have comedy.

Sincerely,


William McCormick

Originally Posted by serpicojr

Surely you understand that common usage of words often differs from technical usage.

No. He doesn’t.

The good news is that he is providing us with comedy.

Originally Posted by William McCormick

I have never argued that the definitions of words have undergone some wild changes. However, I am stating that if the scientific world chose inert, as the definition of the energy of a spinning object.

And wrong again. Inertia in the case of a rotating rigid body is not the definition of the energy. Although it is proportional to it. The rotation energy is E_rot=I/2*omega^2. It depends much more on the angular velocity omega (unit:rad/sec, i.e. 2*pi/sec means one rotation per second = 1 Hertz). Do you see the similarity to the kinetic energy of a moving body ? E_kin=m/2*v^2. This is why inertia is called the rotation analogue of the mass.

Originally Posted by William McCormick

I believe they should shut down, go back and find out what science is. And how important it is. Language experts ought to do the same.

A scientist ought to know English, and English expert ought to know science. That is what destroyed real science.

The usage of words in common language is sloppy and changing with time. In science, every term is clearly and uniquely defined. You just have to learn the definitions like in any other language. Here, "inertia" means "resistance against change of rotational state".

By the way, why should a scientist know English? Why not German, French, Russian, Spanish, Dutch, etc. ? "Real science" is international if not universal and not bound to a particular language. So, what is the real language of science?

Originally Posted by Dishmaster

Originally Posted by William McCormick

I have never argued that the definitions of words have undergone some wild changes. However, I am stating that if the scientific world chose inert, as the definition of the energy of a spinning object.

And wrong again. Inertia in the case of a rotating rigid body is not the definition of the energy. Although it is proportional to it. The rotation energy is E_rot=I/2*omega^2. It depends much more on the angular velocity omega (unit:rad/sec, i.e. 2*pi/sec means one rotation per second = 1 Hertz). Do you see the similarity to the kinetic energy of a moving body ? E_kin=m/2*v^2. This is why inertia is called the rotation analogue of the mass.

Originally Posted by William McCormick

I believe they should shut down, go back and find out what science is. And how important it is. Language experts ought to do the same.

A scientist ought to know English, and English expert ought to know science. That is what destroyed real science.

The usage of words in common language is sloppy and changing with time. In science, every term is clearly and uniquely defined. You just have to learn the definitions like in any other language. Here, "inertia" means "resistance against change of rotational state".

By the way, why should a scientist know English? Why not German, French, Russian, Spanish, Dutch, etc. ? "Real science" is international if not universal and not bound to a particular language. So, what is the real language of science?

The problem started with Benjamin Franklin being laughed out of England as a scientist. Of course his understanding of electricity became, the foundation for everything that America has done. My point is that there were no other countries. Because they were all slaves and fools. America unfortunately slipped back into that category.

When America slipped back into this state. They adopted the same flat world science once again. And flat world math, and English.

When science moved forward it was done in English. No science is coming from another country. Unless they announce and admire the George Washington Benjamin Franklin team that changed the world.

Science may never even come from this country again.

Scientists do not live under law makers.

A spinning object is already not an inertial type energy. It is destroying any inertial, inert energy by spinning. A spinning object has no inert energy.

A spinning object has gyro energy. That gyro energy tends to hold the object in a straight line movement along its axis. But you can then move the spinning object around another object. Not in a straight line.

So I see no correlation between spinning objects and objects moving in a straight line.

You probably have some complicated math formula that may even perform a task, but it is just to far out there, and useless to use safely.

It would be like saying this stuff takes off the paint, here use it. What is it, what is it doing. Why does the can say Nitroglycerin?

Science here in America should only use the English language, and if anything, include a more exacting wording, to insure even the natural use of the word does not become distorted.




http://www.Rockwelder.com/Electricit...nelectrons.jpg
http://www.Rockwelder.com/Electricit...electrons2.JPG



Sincerely,


William McCormick

Originally Posted by William McCormick

When science moved forward it was done in English. No science is coming from another country. Unless they announce and admire the George Washington Benjamin Franklin team that changed the world.

What!? What about Albert Einstein, Max Planck, Marie Curie, Werner Heisenberg, Galileo Galilei, Johannes Kepler, etc. etc.?

Now, this is way too much. Until now, I was tolerating your strange ideas about science. But this is totally narrow minded.

Originally Posted by Dishmaster

Originally Posted by William McCormick

When science moved forward it was done in English. No science is coming from another country. Unless they announce and admire the George Washington Benjamin Franklin team that changed the world.

What!? What about Albert Einstein, Max Planck, Marie Curie, Werner Heisenberg, Galileo Galilei, Johannes Kepler, etc. etc.?

Now, this is way too much. Until now, I was tolerating your strange ideas about science. But this is totally narrow minded.

Germany had about eight guys. That were outrageous. Sticklers for perfection. The individuals around them relayed what they knew to others. Here in America we had about eight guys that were outrageous. And again the people around them conveyed what they knew.

The only problem was that they conveyed it to writers that were not scientists.

Madam Curie found a substance, that was never isolated, by the exacting standards of the time. So you are welcome to believe what you wish, and I will believe what I wish. Until either one of us comes up with some outrageous proof.

Einstein was not considered a scientist by some that did truly outrageous things in science. Including successful space travel. Traveling faster then light. And a few others.

Speaking of proof, check this out. This is the governments idea of proof.



I have spent years trying to get others to get back to real things. Things that will cause controversy and possibly even another revolution. But if Benjamin Franklin did it "so can we" is my motto.

But my point is that years ago I was arguing using standard things as an argument. Getting no where. Doing no good. For fun I said "how about the Bozak particle?"

This bozak came to life one day on a job as we were building a house. A fellow that was new on the job, asked what the technical name for a drilling device was. It was mounted in an extension device, and could bore holes in walls for electric lines.

I told him that it was a self feeding single flute spiral bit in an extension shaft.

So he walked over to my partner and said " I need the, the , ahhh, I don't know the BOZAK extension device!". He was a bit angry for a moment and then it even seemed funny to him. But ever since then the Bozak has always been a term to describe something we did not know the term for.

Do you know when I introduced the bozak particle they started asking what it did, did it spin? If it was my find they thought I should document it. It was very scary to me.



Sincerely,


William McCormick

Originally Posted by William McCormick

As an amateur scientist, I know I cannot put any of this nonsense into the realm of science. It belongs in comedy.

The good news is we have comedy.

Sincerely,


William McCormick

Congratulations! Self-realization is always a good thing.

Originally Posted by (Q)

Originally Posted by William McCormick

As an amateur scientist, I know I cannot put any of this nonsense into the realm of science. It belongs in comedy.

The good news is we have comedy.

Sincerely,


William McCormick

Congratulations! Self-realization is always a good thing.

Thank You, my love of science goes beyond pieces of paper with green ink on them.





Sincerely,


William McCormick