On the composition of finite rotations in \({\mathbb E}^4\) (Q254857)
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scientific article; zbMATH DE number 6556919
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the composition of finite rotations in \({\mathbb E}^4\) |
scientific article; zbMATH DE number 6556919 |
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On the composition of finite rotations in \({\mathbb E}^4\) (English)
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16 March 2016
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The authors investigate products of rotations in the Euclidian space \(\mathbb E^4\). They explain simple and double rotations. Working with real quaternions, the authors give conditions under which the product of two rotations is again a rotation. They use \textit{H. S. M. Coxeter}'s work on quaternions and reflections [Am. Math. Mon. 53, 136--146 (1946; Zbl 0063.01003)]. They also make a number of historical comments; in one of these they refer to Olinde Rodrigues' paper of 1840 on \textit{Transformation groups}.
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Clifford translation
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Gibbs vector
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orthogonal planes
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quaternionic representation
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simple and double rotations
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