# Talk:Axis–angle representation

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Field: Geometry

## Relation with rotation around a fixed axis

I don't see how the subject of this article differs from rotation around a fixed axis. For instance, is there anything which should be in one article and not the other? -- Jitse Niesen (talk) 04:23, 30 January 2007 (UTC)

While the axis angle representation of rotations does describe a rotation around a fixed axis, it is more commonly used to represent general rotations. More importantly, while that article discusses the physics involved in simple rotations, my intention with this article was to focus on how the axis angle representation of rotations is used in robot kinematics, its relationship to other representations of rotations, and its part in the more general concept of displacements. It might turn out that merging them is a better idea, but I'd like to try this as a seperate article first. Kborer 15:57, 30 January 2007 (UTC)
If you look at the axis angle section in rotation matrix it seems that a summary of what I was going to talk about in this article is there. I'd still like to have a more detailed explanation in this article. Kborer 18:42, 30 January 2007 (UTC)
Fair enough. Have a go at it and we'll see how it pans out. Sorry for my rash actions, but I hate having many short and abandoned articles on very similar topics. -- Jitse Niesen (talk) 02:14, 31 January 2007 (UTC)

## Rename article

I propose that the name of this article be changed to "Rotation vector". Kborer (talk) 19:43, 28 December 2007 (UTC)

This name (axis/angle) is widely used in Robotics and Computer Vision for the unit-vector + angle representation. It seems that "rotation vector" is mainly used for the version where the vector magnitude expresses the rotation. Robertmacl (talk) 00:05, 24 September 2012 (UTC)

## Notation for the antisymmetric matrix

I think the notation here is confusing. The 'hat' is so often used to mean a unit vector. Moreover, the usual notation for the relevant matrix is [w]_x. That is, the vector goes in square brackets and a subscript cross is added.

This notation is used, for example, in the definition of the relevant antisymmetric matrix in the article called 'Cross product'. I think for clarity and consistency that same notation ought to be used here.

Is there any special reason to use the 'hat' notation here that I am missing? —Preceding unsigned comment added by 55604PP (talkcontribs) 04:39, 27 January 2010 (UTC)

## Simultaneous orthogonal rotation angle

The Simultaneous Orthogonal Rotation Angle seems to be exactly the same as the rotation vector (the preceding section), as near as I can tell. If you read the papers it seems that the authors also say that it is "a rotation vector", though in such an understated way that it doesn't make clear what their contribution is. If so, it isn't a new representation at all, although it is a new (to me) interpretation of the rotation vector, and reading it did make me think more about the usefulness of the rotation vector as a user-sensible representation. SORA is not exactly original research, since it has been published, but seems highly associated with two authors and has not been widely cited.

Robertmacl (talk) 23:47, 23 September 2012 (UTC)

I thought the same on reading this entry and the associated paper. The authors define the Simultaneous Orthogonal Rotation Angle as the product of angular velocity vector and a duration, which is clearly a standard rotation vector (in the same way that the product of angular acceleration and a duration is angular velocity). I am going to go ahead and remove this section.

64.106.20.136 (talk) 09:10, 19 February 2014 (UTC)

Yes, this had it's own article at one point but that was redirected here as a duplicate. See Talk:Simultaneous orthogonal rotations angle and the associated article history: [1]. Looks like that material was subsequently added here, but it still just duplicates another section so is not needed.--JohnBlackburnewordsdeeds 09:26, 19 February 2014 (UTC)

## axis-angle to quaternion equation notation

I found the notation in the equation for converting from axis-angle to quaternion confusing. $\mathbf{\omega}$ is used to signify the normalized axis of rotation. However, since $\mathbf{w}$ is used in quaternions, this is confusing. Shouldn't $\mathbf{\hat{e}}$ be used to stay with the notation on this page?

Old equation:

$Q = \left(\cos\left(\frac{\theta}{2}\right), \omega \sin\left(\frac{\theta}{2}\right)\right)$

Proposed new equation:

$Q = \left(\cos\left(\frac{\theta}{2}\right), \hat{e} \sin\left(\frac{\theta}{2}\right)\right)$

BAxelrod (talk) 17:41, 16 September 2013 (UTC)