Talk:Rotation

message: Anybody but me notice that the pitch and yaw are mixed up in that 3d model?
:Seems ok, same as e.g. .--Patrick 23:23, 19 September 2005 (UTC)
thread_title: Pitch and yaw

message: The article says Mathematicians consider rotations to be norm-preserving linear transformations on a vector space with an inner product. These form a group of so called special orthogonal matrices.  Is this correct?  Consider the matrix
:\begin{bmatrix} 0  & 1 \\ 1 & 0 \end{bmatrix}
Norm-preserving, right?  Orthogonal, yes.  But special orthogonal?  No, the determinant is -1.  Right? Josh Cherry 14:44, 31 July 2005 (UTC)
replies: text: That is no rotation, but a reflection in the line x=y.--Patrick 23:27, 19 September 2005 (UTC)
replies: text: Right, it's not a proper rotation (it's an improper rotation).  But the article says that any norm-preserving linear transformation is a rotation, and my example preserves norms.  So if rotation means "proper rotation", the article is wrong.  Josh Cherry 00:14, 20 September 2005 (UTC)
replies: text: You are right, I fixed that.--Patrick 02:09, 20 September 2005 (UTC)
thread_title:  Linear transformations 

message: I believe it is wrong that in this general purpose rotation article the mathematical rotation concept is such proeminent — being almost at the beginning of the article and with a lot of math terminology. I would belive that the right order in this article would be (1) hinges, (2) astronomy (3) physics (4) math and (5) amusement rides. 
Also, one should use "three dimensional space" instead of 3D, that one is math and computer graphics jargon, not suitable for this general article. 
The "see also" section needs radical trimming and rearrangement. Oleg Alexandrov (talk) 10:33, 2 November 2005 (UTC)
replies: text: The list of links is a bit long, but the links are all useful, and nicely in alphabetic order.--Patrick 22:16, 2 November 2005 (UTC)

text: I believe this article needs a thorough rethink. I find the stuff in here very arbitrary. I don't think this article can get much worse. Please edit with extreme prejudice. --MarSch 17:13, 2 November 2005 (UTC)
replies: text:  I plan to work on it. I might make big cuts in place. To reply to Patrick above, you don't need to put all the links containing the word "rotation" in this article. Some are more relevant, and some less. Also, now that thanks to MarSch we have some section headings (which do improve the artilce), some links can go in small "see also"s in their most appropriate sections. Oleg Alexandrov (talk) 01:41, 3 November 2005 (UTC)
thread_title:  Order of sections 

message: :An example of rotation of a planar figure around a point is the movement of the propeller of an aircraft.
It does not seem to make sense to model a propeller by a 2D figure.--Patrick 02:44, 5 November 2005 (UTC)
replies: text: If I make it a spinning wheel, will that be better? An aircraft (or, if you wish, a helicopter) propeller is essentially flat. Oleg Alexandrov (talk) 04:16, 5 November 2005 (UTC)

text: If it is flat it does not work. For real objects. even if they are flat, a 3D model is more helpful, with a perpendicular axis; your image will do.--Patrick 09:42, 5 November 2005 (UTC)
replies: text:  Of course a flat propeller will not work! But that's not the point. It is much easier to imagine a 2D rotation than a 3D rotation. I believe it is essential the reader understands 2D rotation first. And yes, a flat propeller is not going to push the airplane forward, but I ask the reader to imagine that there is no airplane or time to start with, just a silly 2D spinning propeller. Oleg Alexandrov (talk) 17:58, 5 November 2005 (UTC)
replies: text: It is a confusing example.--Patrick 20:58, 5 November 2005 (UTC)
thread_title: Propeller

message: There is a lot of discussion on this page recently, see the last three sections above. Now I want to start another one. I would like to cut off the paragraph:
:Rotation is the change of orientation of an object. The term may either refer to the process, or to the resulting change in orientation relative to the starting or reference orientation. If it refers to the process, the simplest case is rotation of a rigid body about a fixed axis of rotation: a line such that each point of the body moves in a plane perpendicular to that line, in a circle centered at the intersection of the plane and the line. 
Here are the reasons: 
* The first sentence is circular. It defines rotation by means of change of orientation, and at that article it defines orientation as result of rotation. It does not give any insight into the article.
::It is not a formal definition but an introductory remark. It mentions the relation with a related concept, and a link to the corresponding article. Those should be kept, of course.--Patrick 20:56, 5 November 2005 (UTC)
replies: text: I think orientation should be fixed so as not to rely on this article. A rotation of an object is a change in the orientation of that object. An orientation is a direction from some fixed point.--MarSch 14:11, 6 November 2005 (UTC)
replies: text: See above. Process means this function t\to \gamma(t); \, \gamma: \mathbb R \to M. The two meanings should be distinguished.--Patrick 20:56, 5 November 2005 (UTC)
replies: text: I don't see any difference between the two meanings. What I think this might be about is that if you turn a rock  in your hands first around one axis and then around another, you might _as well_ have turned it around one axis to arrive at the same final orientation.--MarSch 14:11, 6 November 2005 (UTC)
thread_title:  Removing one paragraph 

message: To facilitate reorganizing the rotation articles, it should first be clear what exists.
*rotation
*Rotation around a fixed axis
*orientation (rigid body)
*Improper rotation
*Quaternions and spatial rotation
*rotation group
*orthogonal group
*Euler's rotation theorem
*Coordinate rotation
*Circular motion
*Rotation matrix
I'm not saying all of this should be merged into one article. Probably not. Please add any articles you think also belong on this list.--MarSch 14:52, 7 November 2005 (UTC)
replies: text: Okay, I think that
*rotation, orientation (rigid body), Rotation around a fixed axis, Improper rotation, axis of rotation should be merged into rotation and orientation.--MarSch 13:13, 8 November 2005 (UTC)

text: Agree with MarSch, mostly: combine rotation, orientation (rigid body), Rotation around a fixed axis, axis of rotation into one. However, Improper rotation should indeed be kept separate. Agree with Oleg, the discussion of SO(n) should be moved to another article or shortened or something. In particular,  Rotation around a fixed axis should never have been split off. It is also rather bizarre and broken in various ways: for example: According to the right-hand rule, moving away from the observer is associated with clockwise rotation Huh ????  linas 14:19, 9 November 2005 (UTC)
replies: text: Have you never heard of that rule?--Patrick 00:05, 10 November 2005 (UTC)
replies: text: *Orbital revolution should be listed as a type of rotation. I also feel that the rotation article should reflect that the term "revolution" is more commonly used for movement of one celestial body around another. 12.106.111.10 19:41, 7 December 2005 (UTC)
replies: text:  I would argue that these details belong in some astronomy-specific articles. And it seems that orbital revolution is already linked from this article. Oleg Alexandrov (talk) 22:39, 7 December 2005 (UTC)
thread_title:  inventory of rotation articles 

message: So, we have rotation as a process, and rotation as a transformation, a distinction which I think is not so important to make as it is clear from the context which one is meant.
I have another question. What exactly is rotation? I would not classify a ball rolling down a hill as rotation, I would think that this movement is more complicated than that. Or am I mistaken? Oleg Alexandrov (talk) 02:05, 9 November 2005 (UTC)
replies: text: Not sure if this is a rhetorical question. In physics terms, the ball is rotating (or pivoting) "instantaneously" about the point of contact (Its also rotating "instantaneoulsy" about any other point as well, but the point of contact is useful because that is where the friction is acting, and where the torque is being imparted.)  In math terms, "instantaneously" just means "tangent space vector" or "derivative". In real life, almost all rotations are constrained in some way: besides rolling and pivoting, there's precessions and torque. Spinning electrons in a magnetic field feel a force; the cosmos, oddly, seems to not be rotating.  So its inappropriate to talk about rotation without talking about these other constraint effects (even though they don't map cleanly onto concepts such as so(n)).linas 14:32, 9 November 2005 (UTC)
replies: text:  Hey Linas, maybe you can write a rotation (physics) article explaining all that, and see how to put a blurb at rotation about this. That would be much appreciated. Oleg Alexandrov (talk) 17:52, 9 November 2005 (UTC)
replies: text:  I will not agree with rotation around a fixed axis being merged into here until we clarify what rotation is all about. I still hope to be convinced that arbitrary rolling or moving around in space is still classified as rotation. Oleg Alexandrov (talk) 01:23, 10 November 2005 (UTC)
thread_title:  What is rotation? 

message: In the caption for the first image, do the two mentions of the word "plane" refer to "airplane" or plane (mathematics)?--GregRM 19:25, 17 February 2006 (UTC)
replies: text: The first, I clarified it.--Patrick 00:52, 18 February 2006 (UTC)
thread_title:  Image caption 

message: Ok – that was an empirical test – now here is a thought experiment to test matters further, from an arbitray inertial frame of reference – imagine the pencil was hollow and full of liquid. If it was spun on just one axis like a centrifuge, the water would adhere to the cylindrical surface like on a spin dryer. If, on the other hand, the pencil was spun like a propeller, the liquid would go to the two ends of the pencil. If you combine these two rotations by starting with a propeller rotation and then adding a centrifuge action, you will get a tendency to get lumps of water shaped like  two rings at the two ends. This  physical effect has two axes of symmetry when viewed from any  inertial frame of reference , due entirely to the rotation of the pencil. These two axes have only a single point in common. This could not be caused by any rotation around a single axis in three dimensions – even an axis continuously moving wrt to the pencil.
: Explain to me then how is it possible that every rotation matrix can be transformed into quaternion or axis/angle representation. I can assure you that matrices and quaternions work perfectly, every 3D video game uses them to make nice realistic rotations. Your thought experiment proves nothing, because it seems that the laws of physics that you imagine work differently that the real ones. The water would not gather into two rings, but would lump at two opposite points at the ends of the cylinder - those two points would lie exactly on the axis of rotation. Anyway, any rotation in any number of dimensions can be described as a rotation of a plane around a fixed point, 'dragging' along the points on planes parrelel to it. That's why in 3D it has to leave one-dimensional axis fixed. 94.101.25.225 (talk) 21:22, 19 April 2009 (UTC)
thread_title: Thought experiment to explore other reference frames

message: Yo, you are the man, I am the badass. Don't be swayed by Archadia's lies! --69.11.210.243 (talk) 20:02, 1 November 2008 (UTC)
thread_title:  Stop reverting my edits 

message: In the thread above (§ Suggest distinguish physical process vs equivalent final orientation), a point is being made that many miss because the terminology is ambiguous.  In an encyclopaedia, it behooves us to clarify ambiguities such as this.  The lead of this article is horrible in this respect.
Who is going to confuse displacement with velocity or path?  We have separate words for them, and realize that they are distinct concepts.  What about their analogues rotation, rotation and rotation?  Oops, we use the same word in each case, and so get confused between them.  The first is expressible as a quaternion (or a rotor in geometric algebra).  The second is a continuous process, best thought of as an instantaneous rate of rotation.  The third is a path generated by a sequence of infinitesimal rotations of the first kind, that result collectively in a rotation of the first kind.  Do others agree that the article needs to distinguish these clearly, and that it currently merely confuses them? —Quondum 17:56, 3 February 2015 (UTC)
thread_title:  Revisiting the distinction 

message: Totally agree with Quondum's note of 17:56, 3 February 2015 (UTC)
thread_title:  Clarifying the ambiguity characterised by Quondum 

message: The physics section of this article should probably mention the concepts of rotational invariance and isotropy, and in particular, the cosmological principle that the laws of physics are invariant under rotations. -- The Anome (talk) 21:16, 15 August 2015 (UTC)
replies: text: -- The Anome (talk) 21:24, 15 August 2015 (UTC)
thread_title:  Rotational invariance 

message: Why and how is this made possible? DaiiZZoo (talk) 08:08, 5 November 2016 (UTC)
thread_title:  Friction relation to Rotation 

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thread_title:  External links modified 

message: This article has serious problems when describing orbits. 
"A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called revolving or orbiting, typically when it is produced by gravity, and the ends of the rotation axis can be called the orbital poles."
There are TWO issues here! 
1) Orbits are not, in general, circular.  Since the definition of "rotation" requires a circular motion, an orbit cannot be a "rotation" as defined in this article. 
2) Even for a perfectly circular orbit, this definition fails.  An orbit is simply a trajectory of a point (see the entry for "orbit" and "trajectory).  Any rotation of the object relative to the stars in a separate rotation about the object's axis.  Calling the circular orbit of a tidally locked moon a "rotation" would say the moon is not rotation on its own axis, which defies the convention of every astronomer.  — Preceding unsigned comment added by Tjfolkerts (talk • contribs) 23:42, 4 February 2021 (UTC)
thread_title:  "Rotation" vs "Orbit" 

message: diff
 – Why limit it to three dimensional objects?
 – The axis is not in the plane.
 – What is this even supposed to mean?
Just plain Bill (talk) 22:46, 25 September 2021 (UTC)
thread_title:  Definition in lead