Answer by Andrew for Why are there only three independent rotations and three...
When people talk about "number of independent rotations" or "number of independent boosts", what they mean is "the number of real-valued parameters you need to specify to uniquely determine a rotation...
View ArticleWhy are there only three independent rotations and three independent boosts?
In what sense, there are only three independent rotations (i.e., rotations $R_x, R_y$, and $R_z$ about $x$, $y$, and $z$ axes, respectively)? Is it because any infinitesimal rotation about an arbitrary...
View ArticleAnswer by RLH for Why are there only three independent rotations and three...
Another way to look at this is that rotations are not specified around axes, but within bivectors.In three dimensions, there are three basis bivectors, canonically $xy$, $yz$, and $zx$, and...
View ArticleAnswer by Eli for Why are there only three independent rotations and three...
The rotation matrix $~\mathbf R_{3\times 3}~$ has 9 direction cosine elements and because $~\mathbf R\,\mathbf R^T\overset{!}{=}\mathbf I_3~$ you obtain 6 constraint equations, this give you 3...
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