Talk:Orientation (rigid body)

From Wikipedia, the free encyclopedia

[edit] orientation

I wonder how standard this "orientation" term is, I confuse it with the other notion of orientation.

It is unfortunate that the word has two meanings, especially because they are sometimes used both in the same context. What else would you call it?--Patrick 10:34, 3 November 2005 (UTC)

Right. However, my question was still whether "orientation" used in this context is standard. Oleg Alexandrov (talk) 15:15, 3 November 2005 (UTC)

Yes, I think so.--Patrick 17:00, 3 November 2005 (UTC)

Yes, the orientation of an object in space is standard informal meaning the direction in which the object is pointed. Don't confuse it with the orientation of vector space basis, which is only an order on the basis vectors.--MarSch 14:25, 6 November 2005 (UTC)

[edit] Question

I don't understand what this article wants to say. The first sentence says that orientation changes by rotation. But what is orientation to start with? This is not clear from the article. Oleg Alexandrov (talk) 03:42, 4 November 2005 (UTC)

The term is so basic that it is hard to find even more basic terms to explain it in. The article explains the relation with another basic term, rotation, and points out that orientation has also another meaning.--Patrick 11:34, 4 November 2005 (UTC)

Wikipedia is not a dictionary, but orientation can be described by the directions of axes fixed in the body.--Patrick 11:48, 4 November 2005 (UTC)

The term "rotation" is also basic, but it has a rigurous math definition eventually, it is an orthogonal matrix with positive determinant. The "orientation" concept must be defined in some rigurous mathematical way too. That something is basic is no excuse not to define it. Pretending for a moment that I don't know what orientation is (and actually, I am not sure I have a good grasp of that concept), this article does not help in explaining it. Oleg Alexandrov (talk) 16:47, 4 November 2005 (UTC)

I added a formal part.--Patrick 23:20, 4 November 2005 (UTC)

Thanks. Oleg Alexandrov (talk) 01:51, 5 November 2005 (UTC)

If you know what a torsor is: the group of rotations is a torsor on the orientations. Basically this means they are isomorphic but NOT canonically. You need to choose a ``starting`` orientation to identify with the unit rotation. Now each rotation corresponds bijectively with an orientation. A rotation describes how to get from one orientation to another.--MarSch 14:43, 6 November 2005 (UTC)