Talk:Rotation representation (mathematics)

From Wikipedia, the free encyclopedia

I am now (slowly) adding the meat to the different headings, but this article is actually revolving (excuse the pun) about rotation representations, not kinematics as such. There is currently no proper comparative page on rotation representations (only on selected single representations), so I suggest that the title might be moved to something similar? Fmalan 20:56, 12 November 2006 (UTC)

Hi, Fmalan, I really appreciate your work here! I was overly ambitious, thinking, "oh, I'll just dash off a note or two about kinematics while I shepherd a few articles through FA" — silly! :( I do intend to add stuff about the rotational velocity and acceleration, though, so perhaps we should fork the article or create a redirect from Representation of orientation (mathematics) or some similar title? Good work! Willow 10:52, 13 November 2006 (UTC)

Sure thing! Thank you for the positive feedback, Willow! This is the first article I am writing (almost) from the ground up. Only a few (very) minor edits to other articles before this, so I am still feeling my way, trying to learn the syntax and such. I am all for a fork. I'm not very knowlegeable about angular rates and accelerations, so I'll stick with the rotation representation (name?) for now. I also have a nifty list of conversion formulas between the representations in this article lined up. Maybe under something like conversion between rotation representations?

[edit] Done!

OK - I've entered everything that I have direct knowledge on... Please feel free to improve from here onwards. Fmalan 18:58, 21 November 2006 (UTC)

Hi Fmalan,

I just logged on and found your "Done!" message — congratulations! :D

The article looks very good! :) I'll probably have to wait a few days to really look it over, though, since I'm trying to get Laplace-Runge-Lenz vector ready for FAC and the objection to Cyclol is still hanging in the air...One thing that strikes me, though, is the plural "representations" — could we change it to "representation"? I'm still a relative newbie, but my impression is that Wikipedia article titles tend to be singular. If you decide that you want to, you can change the title using the "move" button at the top. Many kudos and talk to you soon, Willow 19:34, 21 November 2006 (UTC)

Thanks again for the compliment, Willow. I've got no problem for changes to better adhere to Wikipedia conventions. I created a few redirects to my page. Should I go and manually edit those if I move the page's title (to prevent double redirecting), or will these be automatically changed by Wikipedia's rules? FMalan 08:56, 23 November 2006 (UTC)

You'll have to change them yourself, but only for efficiency. Wikipedia leaves the old page as a REDIRECT to the new page, so clicking on the old link takes you to the right place, cf. Hamilton-Jacobi equations and Hamilton-Jacobi equation. Hoping this helps, :) Willow 12:44, 24 November 2006 (UTC)

[edit] DCM: degrees of freedom vs. rank

Great article. I found the wording of this part a bit confusing: "As Euler's rotation theorem dictates, the DCM has only three degrees of freedom (rank of three), and is a real orthonormal matrix." It seems to imply that the rank is equivalent to or determined by the degrees of freedom, which I don't believe it is. (A 3-DOF 3x3 matrix could also have rank 1 or 2.) The bits about rank and orthonormality, and about linear independence in the next sentence, should probably be moved into the list of DCM properties just below (orthonormality and linear independence are already included in that list). I could be wrong about this though, so I wanted to get some feedback. Hansee 23:56, 28 February 2007 (UTC)

Thanks, Hansee! I agree with your statements. My sentence is rather confusing. A matrix with three degrees of freedom can also be rank 1 or 2, but in this case we are dealing with a rank 3 matrix. It is therefore an "and" rather than an "implies". Feel free to edit, if I don't get around to doing it soon. It is only when one tries to explain a concept to other people that one really understands it well, in my experience. FMalan 09:36, 1 March 2007 (UTC)

[edit] Euler angles - possible confusion

My section on Euler angles have since been edited by a contributor (with paragraphs and matching illustrations removed). I am a bit unhappy about this, since I feel that it illuminated a point of possible confusion. The editor seems to have updated some equations, but not all.

The definition of what I meant with "x-convention" is now no longer there, and care must be taken to ensure that the equations involving the Euler angles are correct. With "x-convention" I referred to non-rotating (intertially fixed) axes of rotation. See the example at Uni Stuttgart.

Wolfram Mathworld seems to decribe the same definition of the x-convention, but then illustrates the example by using co-moving axes. This I find a bit confusing. Please take care! FMalan 09:54, 1 March 2007 (UTC)