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A Great Explanation to What Inertia Tensor is


bbdlqek1

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I appreciate the link and the help. . .

 

A 4 page document on the physics of the inertia tensor isn't a summary. 

 

Not being snarky, I'm just posing the question: If you understood it, can you summarize it?

 

My understanding is this:

it's like a box that frames the physics object with controls on the 6 sides. The values increase/decrease the tension on the controls. In HDTPE, Just For Fun only accepts uniform tension. IOW,  +axis tension is the same as -, and tension on all axis is the same. I don't know if the dll is able to distinguish non-unform values, but even so, the effect difference is minimal from .01 to 99.99 anyway.

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I appreciate the link and the help. . .

 

A 4 page document on the physics of the inertia tensor isn't a summary. 

 

Not being snarky, I'm just posing the question: If you understood it, can you summarize it?

 

My understanding is this:

it's like a box that frames the physics object with controls on the 6 sides. The values increase/decrease the tension on the controls. In HDTPE, Just For Fun only accepts uniform tension. IOW,  +axis tension is the same as -, and tension on all axis is the same. I don't know if the dll is able to distinguish non-unform values, but even so, the effect difference is minimal from .01 to 99.99 anyway.

 

Well I think for a summary that tries to summarize inertia tensor with the least amount of equation and terminology, 4 documents are really short.

Since you don't look satisfied with even Dan's explanation and you don't seem to have understood it properly, even though I'm not good with words like Dan and I'm not a native english speaker, I'll try my best to explain it to you but keep this in mind, I'm not going to explain things about inertia tensor that are already in Dan's summary.

 

It's basically about the inertia of rotational movement that corresponds with the mass in translational motion.

so that's the reason why Dan Morris used below 2 equations and compared these 2 equations to explain and show the similarities in these equations.

 

 τ = I *dω , F=m*a 

 

omega (w) is the angular velocity so if you differentiate it with respect to time (dw) you will get angular acceleration which plays very similar role with translational acceleration (a).

 

Rotational force, T (torque) which is the cross producted physical quantity of radius and force (rxF), plays very similar role with translational force (F).

 

And as you see, in rotational motion, Inertial Moment(I)'s role corresponds to mass (m).

 

So the higher Inertial moment a rigid body has the more rotational force you need to apply to give the same angular acceleration. 

If you understand these I believe you will understand what H also is and its role in the equation H=I(Inertial Moment)*w

 

Since angular momentum(H)'s x component is related to not only x angular velocity but also y and z (If you wanna know why, read Dan's summary. You will find an example (asymmetric sphere rotation) he used to explain this), you need 3 squared number of combinations of inertia tensors in total to describe the angular movement. Thus, there are 9 types of inertia tensors (Ixx Ixy Ixz Iyy .......)

However since inertia tensor is symmetric tensor, Ixy=Iyx, Ixz=Izx, Iyz=Izy. Therefore there are only 6 types of tensors that are independent.

This is the reason why you see these set of tensors appear as a hexahedron in visible geometric shape.

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Great, now I feel even dumber when it comes to hdt (and I thought I was doing ok with it)... Doesn't anyone ever attempt to explain it in laymans -explainittothevillageidiotoverthere- terms rather than requiring a masters in physics just to begin to understand it? 

 

 

 

Well I think for a summary that tries to summarize inertia tensor with the least amount of equation and terminology, 4 documents are really short. Since you don't look satisfied with even Dan's explanation and you don't seem to have understood it properly, even though I'm not good with words like Dan and I'm not a native english speaker, I'll try my best to explain it to you but keep this in mind, I'm not going to explain things about inertia tensor that are already in Dan's summary.

 

I'm not one to ask questions before attempting to find my own answers and I'm sure you didn't mean to come off as pompous as it sounded, but this is why people who can't figure this stuff out make it worse for themselves (besides the umpteen variables when it comes to weight, size and speed); they're intimidated... because not everyone is a math wiz and when they do come with questions, this is the types of responses they get.

 

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Great, now I feel even dumber when it comes to hdt (and I thought I was doing ok with it)... Doesn't anyone ever attempt to explain it in laymans -explainittothevillageidiotoverthere- terms rather than requiring a masters in physics just to begin to understand it? 

 

 

 

Well I think for a summary that tries to summarize inertia tensor with the least amount of equation and terminology, 4 documents are really short. Since you don't look satisfied with even Dan's explanation and you don't seem to have understood it properly, even though I'm not good with words like Dan and I'm not a native english speaker, I'll try my best to explain it to you but keep this in mind, I'm not going to explain things about inertia tensor that are already in Dan's summary.

 

I'm not one to ask questions before attempting to find my own answers and I'm sure you didn't mean to come off as pompous as it sounded, but this is why people who can't figure this stuff out make it worse for themselves (besides the umpteen variables when it comes to weight, size and speed); they're intimidated... because not everyone is a math wiz and when they do come with questions, this is the types of responses they get.

 

I know I really suck at explaining things so I'm sorry if I sounded pompous to you but I tried my best to explain inertia tensor in the way it is  :dodgy:

You know there are prerequired knowledges to everything we learn and when we try to learn something without prerequired knowledges, that's where the problem begins.

I think these videos can help you understand better what inertia tensor is.

 

What is a Tensor? - 

Rotational inertia and tumbling - 

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Thanks for the videos bbdlqek1, and I will concur with you that understanding this kind of stuff requires a person to have prior mathematical knowledge or at least a good upper-level understanding of how motion works. Even after watching the videos I can see how a person not well educated in advanced science and mathematics can get lost real fast. I was having college-day engineering flashbacks just watching them!

 

There is no straight-forward layman's terms on angular inertia tensors without having to understand how 3-dimensional motion works; and to understand how 3-d motion works, you'll have to understand how 2-d motion works; and to understand how 2-d motion works, you'll have to understand how 1-d motion works. All the knowledge builds off each other, and each can be represented through mathematical functions and matrices. Throw in certain scaling to adjust for the units of measure on what HDTPE uses, and you can see how complex it may get.

 

Though I understand the math behind it, I usually go the guess, test, rinse-and-repeat method to find magical numbers. In terms of refining though, it would be best to understand the mathematics.

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Thanks for the videos bbdlqek1, and I will concur with you that understanding this kind of stuff requires a person to have prior mathematical knowledge or at least a good upper-level understanding of how motion works. Even after watching the videos I can see how a person not well educated in advanced science and mathematics can get lost real fast. I was having college-day engineering flashbacks just watching them!

 

There is no straight-forward layman's terms on angular inertia tensors without having to understand how 3-dimensional motion works; and to understand how 3-d motion works, you'll have to understand how 2-d motion works; and to understand how 2-d motion works, you'll have to understand how 1-d motion works. All the knowledge builds off each other, and each can be represented through mathematical functions and matrices. Throw in certain scaling to adjust for the units of measure on what HDTPE uses, and you can see how complex it may get.

 

Though I understand the math behind it, I usually go the guess, test, rinse-and-repeat method to find magical numbers. In terms of refining though, it would be best to understand the mathematics.

 

Thank you Jacques00 for your kind words. I totally agree with your trial and error method and I think its hands down the best way at finding the magical numbers. Though, I believe having better understanding or intuition at these kind of stuffs in some cases can really help you reduce time and efforts put into finding the magical numbers. 

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Thank you Jacques00 for your kind words. I totally agree with your trial and error method and I think its hands down the best way at finding the magical numbers. Though, I believe having better understanding or intuition at these kind of stuffs in some cases can really help you reduce time and efforts put into finding the magical numbers. 

 

So true, and I understand wholeheartedly. For me, one side of my brain wants to dissect it and find out how it works and get the numbers exactly right, but the other side just wants to make it look good and leave it at that... so I have to hit a middle ground somewhere. With that, I kind of live by the philosophy of "whatever works!" and if it doesn't work, fix it until it's close enough!

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look at this thing

http://giant.gfycat.com/ClearcutMajesticCirriped.gif

 

It's some lights that are hooked up to a 3 axis gyro.

 

Now imagine, like a spinning top, a big flat top will take more force to get it to spin than a skinny top.  Have you ever seen a figure skater put her arms up and she starts spinning faster, and when she wants to stop, she sticks her arms, head and leg out?  It's like that.  The farther your weight is from the axis you are spinning around, the more force it will take for you to keep spinning at the same speed.

 

Now superimpose 3 figure skaters on top of each other, along the x,y and z axis.  (light the light thingy I linked to)  you have to calculate how far out the arms are of each of the three figure skaters and then make the rotational force of each one work to affect the other two.

 

tl:dr

Don't worry too much about those settings unless you want to apply physics to a discrete object like a cart or a bag or something.  If your object is attached to an immovable object  (like hair stuck to a head, or boobs stuck to a torso)  The tensors should be completely neutral, since the head/torso/etc should anchor the rotation of the object if it is trying to be realistic.

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The smartest people can explain things in the simplest terms, because they realize trying to sound smart isn't the point.  The best explenations would probably go something like "Well, if you raise this variable, this happens... if you lower it, that happens".  You know, like you think we should learn something practical :D

I don't want to be rude here but please don't make me laugh. Even if you have exactly the same values of inertia tensors but the mass is different, the angular movement will be different so you can't just go "Oh if you raise this variable this happens. if you lower it that happens". These variables just don't work in that way. Please do some kind of research before you speak out complete nonsense. If my explanations and the one I uploaded are too much for you that it looks like I'm trying to sound smart and you think the variables can be explained in layman's terms without using any integrals and that's the explanation you're looking for, I'm sorry to say this but you better stay away from this and stick to learning things you call "simple" and "practical".

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I think some are forgetting that this is HDT Physics Extension. You can't explain physics in terms of "twist this knob that way and this is what happens". It just doesn't work that way. I understand just enough of the concepts and math to be dangerous, but not enough to really understand most of this, and certainly not enough to explain it to anyone else. So, sorry to break this to you, but some things just don't have simple explanations, with physics being a perfect example. And if you hated math in school, then really, just twiddle the knobs and see what happens. And even then, a lot will depend on the particular skeleton you're using and how the pivots are set up (not to mention the skin weighting of the mesh you're working with), as someone was kind enough to point out to me when I asked a somewhat related question regarding axes.

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