Talk:Euler's theorem (rotation): Difference between revisions
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imported>Jitse Niesen (what is a rotation?) |
imported>Paul Wormer |
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:<math> \bold{x} \mapsto \bold{Rx} + \bold{b} </math> | :<math> \bold{x} \mapsto \bold{Rx} + \bold{b} </math> | ||
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) | |||
Revision as of 05:23, 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. --Paul Wormer 11:23, 14 May 2009 (UTC)