The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections
Open accessAbstract
This paper reviews the Euler–Rodrigues formula in the axis–angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler–Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler–Rodrigues parameters and the Euler–Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler–Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics.
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Cites
A Mathematical Introduction to Robotic Manipulation
Murray, R. M., Li, Z., & Sastry, S. S. (2017) · CRC Press eBooks · doi:10.1201/9781315136370 · Cited by 6,694
Closed-form solution of absolute orientation using unit quaternions
Horn, B. K. P. (1987) · Journal of the Optical Society of America A · doi:10.1364/josaa.4.000629 · Cited by 4,116
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Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
Marsden, J. E., & Ratiu, T. S. (1999) · Texts in Applied Mathematics · doi:10.1007/978-0-387-21792-5 · Cited by 2,961
A Mathmematical Introduction to Robotic Manipulation
Murray, R. M., Li, Z., & Sastry, S. (1994) · Cited by 2,676
McKerrow, P. J. (1991) · Medical Entomology and Zoology · Cited by 1,731
Animating rotation with quaternion curves
Shoemake, K. (1985) · ACM SIGGRAPH Computer Graphics · doi:10.1145/325165.325242 · Cited by 1,719
Mathematical elements for computer graphics
Rogers, D. F., & Adams, J. A. (1976) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,072
Geometric Algebra for Physicists
Doran, C., & Lasenby, A. (2003) · doi:10.1017/cbo9780511807497 · Cited by 962
Fulton, W., & Harris, J. (2004) · Graduate Texts in Mathematics · doi:10.1007/978-1-4612-0979-9 · Cited by 787
Metadata
- Authors
- Dai, J. S.
- Venue
- Mechanism and Machine Theory
- Publisher
- Elsevier BV
- Published
- 2015-10
- Volume
- 92
- Pages
- 144-152
- ISSN
- 0094-114X (ISSN-L)
- OpenAlex
- W2202678121
- Cited by
- 367
- References
- 31
- FWCI
- 24.97
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Dai, J. S. (2015). Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections. Mechanism and Machine Theory. https://doi.org/10.1016/j.mechmachtheory.2015.03.004
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
