Talk:Euler's theorem (rotation)

What is a rotation?

As I understand the first sentence, a rotation is defined to be "a motion of the rigid body that leaves at least one point of the body in place", but what is a rigid body motion? I think SE(3), i.e., all transformations of the form

${\mathbf {x}}\mapsto {\mathbf {Rx}}+{\mathbf {b}}$

with R in SO(3), however that does not seem to be what is meant in the article. -- Jitse Niesen 10:50, 14 May 2009 (UTC)

Yes, when b = 0 it is a rotation, provided R is an orthogonal matrix. When R = E it is a pure translation. I thought that "rigid body motion" would not have to be defined. See also Rotation matrix where I wrote the same (I'm still working on the latter). --Paul Wormer 11:23, 14 May 2009 (UTC)