This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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)
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 ( talk • contribs) 04:39, 27 January 2010 (UTC)
Whatever notation is used, the formula for exp(omega-tilda) we should remind the reader of the definition of omega as theta times u, e.g., by changing "exp(omega-tilda)" to "exp(omega-tilda) = exp(theta u-tilda). In the same formula, u-dot-L should be replaced by u-tilda (if the current tilda-notation is retained). — Preceding unsigned comment added by Tthrall ( talk • contribs) 16:25, 27 June 2015 (UTC)
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)
I found the notation in the equation for converting from axis-angle to quaternion confusing. is used to signify the normalized axis of rotation. However, since is used in quaternions, this is confusing. Shouldn't be used to stay with the notation on this page?
Old equation:
Proposed new equation:
BAxelrod ( talk) 17:41, 16 September 2013 (UTC)
Couldn't fit in the edit summary for this edit, so writing it here.
M∧Ŝ c2ħε Иτlk 17:17, 3 October 2015 (UTC)
In the article Rotation group SO(3), the Lie algebra so(3) is defined as the set of skew-symmetric matrices. Here, it is defined as the vector space .
In my opinion, since , the Lie algebra so(3) should be defined as in the cited article and not as in this one.
Joan Solà ( talk) 23:01, 23 December 2016 (UTC)
Maybe I am wrong, but my argument goes like this. so(3), the Lie algebra of SO(3), is the tangent space (one can look at it as the time derivative, or the velocity space) of SO(3) at the origin, and this gives the set of skew symmetric matrices. This vector space so(3) is indeed equivalent (isomorphic) to R3, since it is a vector space with 3 DoF. But this does not mean that R3 is the Lie algebra, it is just a vector space isomorphic to the Lie algebra. Of course due to this isomorphism one can abuse language and call R3 also the Lie algebra. But I think this is not accurate: R3 is not the derivative of SO(3) at the origin. Derivating 3x3 matrices with respect to time, you will always get a 3x3 matrix, and never a 3-vector.
The same goes for the exponential and logarithmic maps. If v is of R3, then exp(v) is not a rotation matrix (who knows what it is). Only exp(S(v)), with S(v) a skew-symmetric matrix isomorphic to v, can be called a member of SO(3) such that R=exp(S(v)). Again, one can abuse the language and say R = exp(v). Indeed, many people do. But this does not make it proper.
So my claim is basically a terminology claim. I am, however, not 100% convinced that R3 cannot be called properly the Lie algebra of SO(3).
Joan Solà ( talk) 21:57, 9 September 2019 (UTC)