Talk:Euler's theorem (rotation): Difference between revisions
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with '''R''' in SO(3), however that does not seem to be what is meant in the article. -- [[User:Jitse Niesen|Jitse Niesen]] 10:50, 14 May 2009 (UTC) | with '''R''' in SO(3), however that does not seem to be what is meant in the article. -- [[User:Jitse Niesen|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. --[[User:Paul Wormer|Paul Wormer]] 11:23, 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). --[[User:Paul Wormer|Paul Wormer]] 11:23, 14 May 2009 (UTC) | ||
Revision as of 05:34, 14 May 2009
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
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)