Research Article

On the Composition of Rotations in $\mathbb{R}^3$

Volume: 8 Number: 4 December 8, 2025
François Dubeau *
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences

On the Composition of Rotations in $\mathbb{R}^3$

Abstract

Euler stated that the composition of two successive rotations is also a rotation, but did not solve the problem of finding the resultant (axis and angle of rotation) of the composition. It is Rodrigues who solved it. Based on the Rodrigues' formula for a rotation in $\mathbb{R}^3$, we present a unified new proof of both Euler's existence theorem and Rodrigues' identification. The proof relies only on basic algebraic properties of vectors in $\mathbb{R}^3$.

Keywords

Composition, Rotation formula, Vector analysis

References

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  7. [7] M. F. Maritz, Rotations in three dimensions, SIAM Rev., 63(2) (2021), 395-404. http://dx.doi.org/10.1137/19M128867X
  8. [8] O. Rodrigues, Des lois géométriques qui régissent les déplacements d’un objet solide dans l’espace, et de la variation des coordonnées provenant de ces déplacements considérées indépendamment des causes qui peuvent les produire, J. Math. Pures Appl., 5 (1840), 380-440.
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Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Early Pub Date

December 3, 2025

Publication Date

December 8, 2025

Submission Date

April 23, 2025

Acceptance Date

November 9, 2025

Published in Issue

Year 2025 Volume: 8 Number: 4

DOI

https://doi.org/10.33434/cams.1682530

IZ

https://izlik.org/JA35GK79SU

Cite

RIS / Bibtex
APA
Dubeau, F. (2025). On the Composition of Rotations in $\mathbb{R}^3$. Communications in Advanced Mathematical Sciences, 8(4), 183-188. https://doi.org/10.33434/cams.1682530
AMA
1.Dubeau F. On the Composition of Rotations in $\mathbb{R}^3$. Communications in Advanced Mathematical Sciences. 2025;8(4):183-188. doi:10.33434/cams.1682530
Chicago
Dubeau, François. 2025. “On the Composition of Rotations in $\mathbb{R}^3$”. Communications in Advanced Mathematical Sciences 8 (4): 183-88. https://doi.org/10.33434/cams.1682530.
EndNote
Dubeau F (December 1, 2025) On the Composition of Rotations in $\mathbb{R}^3$. Communications in Advanced Mathematical Sciences 8 4 183–188.
IEEE
[1]F. Dubeau, “On the Composition of Rotations in $\mathbb{R}^3$”, Communications in Advanced Mathematical Sciences, vol. 8, no. 4, pp. 183–188, Dec. 2025, doi: 10.33434/cams.1682530.
ISNAD
Dubeau, François. “On the Composition of Rotations in $\mathbb{R}^3$”. Communications in Advanced Mathematical Sciences 8/4 (December 1, 2025): 183-188. https://doi.org/10.33434/cams.1682530.
JAMA
1.Dubeau F. On the Composition of Rotations in $\mathbb{R}^3$. Communications in Advanced Mathematical Sciences. 2025;8:183–188.
MLA
Dubeau, François. “On the Composition of Rotations in $\mathbb{R}^3$”. Communications in Advanced Mathematical Sciences, vol. 8, no. 4, Dec. 2025, pp. 183-8, doi:10.33434/cams.1682530.
Vancouver
1.François Dubeau. On the Composition of Rotations in $\mathbb{R}^3$. Communications in Advanced Mathematical Sciences. 2025 Dec. 1;8(4):183-8. doi:10.33434/cams.1682530

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