Talk:Rotation formalisms in three dimensions

Formula to compute Euler angles from matrix uses two different conventions

This is a cross-post from Wikipedia:Reference desk/Mathematics#Formula_to_compute_Euler_angles_messed_up (soon to be Wikipedia:Reference desk/Archives/Mathematics/2012 July 11#Formula_to_compute_Euler_angles_messed_up).

Rotation formalisms in three dimensions#Conversion_formulae_between_formalisms describes how to compute Euler angles of a rotation from the rotation matrix. The formulas in that section use different conventions for the Euler angles within that same section. Indeed, the article mentions rotating around zxz for the first formula, and rotating around xyz for the second formula. Indeed, you can see the two formulas can't be consistent for the first formula claims that θ = arccos(A₃₃), whereas the last one claims A₃₃ = cos(φ)cos(θ), and A₃₁ = sin(θ).

Could you figure out the correct formulas for a single convention and fix the article? Thanks in advance.

– b_jonas 22:47, 11 July 2012 (UTC)

You are right. I already twice draw attention to the fact that this article is partially false , but without success . It should be coordinated with the Euler angles article. That is a lot of work and I will not begin it without support from other editors involved. Chessfan (talk) 18:41, 16 July 2012 (UTC)

Sorry I made an édit error with your title Chessfan (talk) 18:52, 16 July 2012 (UTC)

See http://www.soi.city.ac.uk/~sbbh653/publications/euler.pdf Chessfan (talk) 08:05, 18 July 2012 (UTC)

Have to second this post, since

${\begin{aligned}\phi &=\operatorname {arctan2} (A_{31},A_{32})\\\theta &=\arccos(A_{33})\\\psi &=-\operatorname {arctan2} (A_{13},A_{23})\end{aligned}}$

and

${\begin{array}{lcl}\mathbf {A} &=&{\begin{bmatrix}\cos \theta \cos \psi &\cos \phi \sin \psi +\sin \phi \sin \theta \cos \psi &\sin \phi \sin \psi -\cos \phi \sin \theta \cos \psi \\-\cos \theta \sin \psi &\cos \phi \cos \psi -\sin \phi \sin \theta \sin \psi &\sin \phi \cos \psi +\cos \phi \sin \theta \sin \psi \\\sin \theta &-\sin \phi \cos \theta &\cos \phi \cos \theta \\\end{bmatrix}}\end{array}}$

does not fit together. 212.222.53.78 (talk) 15:45, 10 October 2013 (UTC)

Again, I think the article I mentioned above is OK .Chessfan (talk) 23:47, 25 January 2014 (UTC)

https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f184f89aa7fe5cdbeb6f368c9b7c859abf4802

The matrix above is for left-hand system, not right-hand. — Preceding unsigned comment added by 82.33.216.70 (talk) 11:05, 7 February 2017 (UTC)

Gibbs vector

Would someone please redirect Gibbs vector to this page? 75.139.254.117 (talk) 03:38, 30 December 2016 (UTC)

done --Rainald62 (talk) 15:07, 13 August 2018 (UTC)

Proposed merge of Three-dimensional rotation operator into Rotation formalisms in three dimensions

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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same concept fgnievinski (talk) 05:45, 17 May 2023 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Three-dimensional rotation operator can just be deleted. It doesn't say anything independently interesting. –jacobolus (t) 01:41, 21 January 2024 (UTC)

"angle-angle-angle" section was a mess

I just deleted the "Angle-angle-angle" section, which user:D3x0r added in 2020 originally under the name "Quaternion Natural Log" in a few edits special:diff/966425539/970789404. This section was substantially redundant with the previous portions of the article, particularly § Euler axis and angle (rotation vector), because the so-called rotation vector (properly a bivector) is the logarithm of a rotor ("unit quaternion"). We could add some text somewhere discussing the logarithm of a rotor or a rotation matrix, but duplicating a bunch of formulas into two different sections of the article in an expansive, completely unsourced formulary is just confusing to readers. –jacobolus (t) 19:18, 9 September 2024 (UTC)

https://en.wikipedia.org/wiki/Bispinor this doesn't look like R3; or 3 real numbers. This is meant to be Euler Axis to Euler Axis; there's two operations, to rotate a point around the axis, and to rotate a Euler Axis around a Euler Axis. But additionally, the rotation of a rotation can either be intrinsic or extrinsic (That's what I call them, the axis can be external to the rotating axis, like a rocket spinning along it's length, but spun on a stick at some other direction is an external rotation, or the rotation really happens from outside the rotating frame. The other is the thrusters on the rocket itself that are generating a torque, and their applied rotation to the rocket's rotation changes as the rocket rotates, and is internal to the frame, or part of the frame of the rocket. The difference between the two is the direction of the cross product in the Rodrigues Forumla.

I have this original copy, minus a few minor edits... https://github.com/d3x0r/STFRPhysics/blob/master/wikipedia.wiki is there any hope to save the article? Can we collaborate to get those few formula integrated with the rest of the article?

Euler Axis is additive, in the context that the various torques generated by engines expressed as Euler Axis (angle*axis resolved) can just be added together. Rotations that happen at the same time to a thing are additive; and with subtraction you can find the missing axis-angle you would have additionally needed to get to where you are that you didn't have... But it should be an extra article maybe? With Original Research Tagged on it? D3x0r (talk) 22:52, 24 September 2024 (UTC)

I'm having a lot of trouble understanding what you are trying to say. Do you have a source which elaborates, e.g. a published paper somewhere? –jacobolus (t) 02:22, 25 September 2024 (UTC)