Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations
ABSTRACT The need to use rotations occurs very often in different domains. We present a basic extensive treatment of rotations in 3D. The results are presented and derived in a coordinate‐free setting, where no frames are required and no components of any matrix are manipulated. We start with the di...
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| Format: | Article |
| Language: | English |
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Wiley
2025-01-01
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| Series: | Engineering Reports |
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| Online Access: | https://doi.org/10.1002/eng2.13107 |
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| author | François Dubeau |
| author_facet | François Dubeau |
| author_sort | François Dubeau |
| collection | DOAJ |
| description | ABSTRACT The need to use rotations occurs very often in different domains. We present a basic extensive treatment of rotations in 3D. The results are presented and derived in a coordinate‐free setting, where no frames are required and no components of any matrix are manipulated. We start with the direct problem of establishing the finite rotation formula. Then we consider the composition and the vector decomposition of finite rotations. We conclude the paper by considering the inverse problem namely finding the axis of rotation and the angle of rotation from its effect on vectors. |
| format | Article |
| id | doaj-art-c79004bb8dba4ed8aaae580e6eb90798 |
| institution | Kabale University |
| issn | 2577-8196 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Engineering Reports |
| spelling | doaj-art-c79004bb8dba4ed8aaae580e6eb907982025-01-31T00:22:49ZengWileyEngineering Reports2577-81962025-01-0171n/an/a10.1002/eng2.13107Composition, Non‐Commutativity, and Vector Decompositions of Finite RotationsFrançois Dubeau0Département de mathématiques Université de Sherbrooke Sherbrooke CanadaABSTRACT The need to use rotations occurs very often in different domains. We present a basic extensive treatment of rotations in 3D. The results are presented and derived in a coordinate‐free setting, where no frames are required and no components of any matrix are manipulated. We start with the direct problem of establishing the finite rotation formula. Then we consider the composition and the vector decomposition of finite rotations. We conclude the paper by considering the inverse problem namely finding the axis of rotation and the angle of rotation from its effect on vectors.https://doi.org/10.1002/eng2.13107compositionfinite rotation formulanon‐commutativityvector decomposition |
| spellingShingle | François Dubeau Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations Engineering Reports composition finite rotation formula non‐commutativity vector decomposition |
| title | Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations |
| title_full | Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations |
| title_fullStr | Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations |
| title_full_unstemmed | Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations |
| title_short | Composition, Non‐Commutativity, and Vector Decompositions of Finite Rotations |
| title_sort | composition non commutativity and vector decompositions of finite rotations |
| topic | composition finite rotation formula non‐commutativity vector decomposition |
| url | https://doi.org/10.1002/eng2.13107 |
| work_keys_str_mv | AT francoisdubeau compositionnoncommutativityandvectordecompositionsoffiniterotations |