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perfect sphere with mass in space


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#1 lomateron   Members   -  Reputation: 363

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Posted 11 January 2013 - 12:53 AM

Analyzing a perfect physical sphere in space I see it having two kinds of movements, one will be defining the center position of the sphere in 3D space with a velocity that will not change unless there is a force, and the other is the rotation of the sphere, this is the part that i still dont fully understand.

What i think is that this rotation will have 3 axis and like the translation has a velocity that doent change without a force, the sphere will have too a velocity of rotation defined in those three axis that doesnt change unless there is a force.

After seeing how the earth moves around the sun I can say that a perfect sphere in space is not limited to rotate around a fixed axis.

Can I describe all possible ways a sphere can rotate (forever unless there is a force) defining a velocity in those 3 axis?


Edited by lomateron, 11 January 2013 - 01:28 AM.


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#2 Ashaman73   Crossbones+   -  Reputation: 7987

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Posted 11 January 2013 - 01:35 AM

Edit: lomateron talked about velocity and not force => Alvaro

 

You are talking about torque, and yes, 3 axis are more than enough, in fact, every possible rotation in 3d can be described as a rotation around a single vector (axis). This is very helpful, because you can compress a rotation into a vector and an angle. The mathematically construct of this is called quaternion.


Edited by Ashaman73, 11 January 2013 - 02:43 AM.


#3 Álvaro   Crossbones+   -  Reputation: 13897

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Posted 11 January 2013 - 02:07 AM

You are talking about torque, and yes, 3 axis are more than enough, in fact, every possible rotation in 3d can be described as a rotation around a single vector (axis). This is very helpful, because you can compress a rotation into a vector and an angle. The mathematically construct of this is called quaternion.

 

No, he is talking about angular velocity, which is not a rotation, but a pseudo-vector, and that pseudo-vector is three-dimensional. (For the more mathematically savvy people in the forum: Rotations form a Lie group and angular velocity is an element of the corresponding Lie algebra.)

 

I think the answer the OP is looking for is that position, velocity, attitude (that one is a rotation) and angular velocity are enough to describe the state of a solid object in mechanics, as he initially thought. Whatever extra things the Earth does have to do with external forces.


Edited by Álvaro, 11 January 2013 - 02:11 AM.


#4 0r0d   Members   -  Reputation: 819

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Posted 11 January 2013 - 02:44 AM

After seeing how the earth moves around the sun I can say that a perfect sphere in space is not limited to rotate around a fixed axis.

 

The Earth is not a perfect sphere, nor is it a perfectly rigid body with uniform density, or any of that.  It sounds like you want math more suited to billiard balls, not planets.



#5 lomateron   Members   -  Reputation: 363

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Posted 11 January 2013 - 03:10 AM

The earth example was to show that a fixed axis of rotation isnt enought to descibe all kinds of that rotation that can go forever on a sphere in space, in the earth example it is rotating around an axis and the axis is rotationg around another axis (and i think that axis movement is forever).

Can I describe that rotational movement that can go forever in asphere with a magnitude in those fixed 3 axis(image)?

UBJAR.png


Edited by lomateron, 11 January 2013 - 03:14 AM.


#6 Álvaro   Crossbones+   -  Reputation: 13897

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Posted 11 January 2013 - 03:17 AM

Perhaps my earlier answer wasn't clear enough: In the absence of external forces, the angular velocity is all you need to describe how an object rotates forever. The Earth does all sorts of funny things because there are external forces. See this Wikipedia page for details.



#7 Bacterius   Crossbones+   -  Reputation: 9263

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Posted 11 January 2013 - 03:18 AM

in the earth example the axis is moving too

Moving in relation to what? You need a frame of reference to define motion, both translation and rotation.


The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis


#8 Álvaro   Crossbones+   -  Reputation: 13897

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Posted 11 January 2013 - 03:20 AM

in the earth example the axis is moving too

 

Moving in relation to what? You need a frame of reference to define motion, both translation and rotation.

 

I am not sure that's true. At least in Newtonian mechanics, there is a notion of an inertial frame of reference, and rotations are the same under all inertial frames of reference.



#9 lomateron   Members   -  Reputation: 363

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Posted 11 January 2013 - 03:32 AM

so the axis "rotating" aroung another axis is because the earth isnt a perfect sphere, ok i undestand it now, the precessin of the erath was making me think a perfect sphere could move in rare ways.


Edited by lomateron, 11 January 2013 - 04:02 AM.


#10 Álvaro   Crossbones+   -  Reputation: 13897

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Posted 11 January 2013 - 04:03 AM

so the axis "rotating" aroung another axis is because the earth isnt a perfect sphere, ok i undestand it now, the precessin of the erath was making me think a perfect sphere could move in rare ways.

 

No, it's because there are external forces acting on Earth. Read the Wikipedia page I linked to earlier.



#11 Olof Hedman   Crossbones+   -  Reputation: 2948

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Posted 11 January 2013 - 07:56 AM

The Earth is not a perfect sphere, nor is it a perfectly rigid body with uniform density, or any of that.  It sounds like you want math more suited to billiard balls, not planets.

 

Pretty darn close though. The earth is in fact smoother then a billiard ball, but it's slightly squashed at the poles.. not that much though, so you probably wouldn't notice it unless you are a professional pool player :)



#12 Bacterius   Crossbones+   -  Reputation: 9263

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Posted 11 January 2013 - 03:23 PM

I am not sure that's true. At least in Newtonian mechanics, there is a notion of an inertial frame of reference, and rotations are the same under all inertial frames of reference.

 

Mhh. You may be right. My intuition was that if you are rotating in empty space with no point of reference, you cannot know you are rotating, whereas if you have a point of reference which is not stationary under your own frame of reference (isn't orbiting around you at the same rate you are rotating) then you can be aware of your rotational motion, so rotation is also a relative quantity, but I am probably wrong - I was never that good at rotational mechanics.


Edited by Bacterius, 11 January 2013 - 03:24 PM.

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis


#13 lomateron   Members   -  Reputation: 363

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Posted 11 January 2013 - 03:27 PM

Yes it's because it's not perfect, so the external forces(sun and moon) can apply that forces to that bumped places.

#14 Álvaro   Crossbones+   -  Reputation: 13897

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Posted 11 January 2013 - 03:33 PM


I am not sure that's true. At least in Newtonian mechanics, there is a notion of an inertial frame of reference, and rotations are the same under all inertial frames of reference.

 
Mhh. You may be right. My intuition was that if you are rotating in empty space with no point of reference, you cannot know you are rotating, whereas if you have a point of reference which is not stationary under your own frame of reference (isn't orbiting around you at the same rate you are rotating) then you can be aware of your rotational motion, so rotation is also a relative quantity, but I am probably wrong - I was never that good at rotational mechanics.
 
 
 



You can tell that the Earth is rotating in several ways. Of the top of my head:
* The Coriolis effect.
* You can see stars and distant galaxies apparently rotating around you (and they would be traveling at superluminar speeds).
* Foucault's pendulum works.
* The Earth is wider around the equator because of the centrifugal force created by its rotation.

Edited by Álvaro, 11 January 2013 - 03:41 PM.





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