Abstract
Lineer bir dönüşüm aynı zamanda self-inverse (tersi
kendisine eşit) ve anti-homomorfik ise involüsyon; self-inverse ve homomorfik
ise anti-involüsyondur. Üç-boyutlu Öklid uzayı teki vida
hareketleri dual-kuaterniyonlar ile elde edilen (anti)-involüsyon dönüşümleri
ile verilebilir. Biz bu çalışmada, dual-kuaterniyonları kullanarak ikisi
involüsyon dönüşüme diğer ikisi ise anti-involüsyon dönüşüme karşılık gelen
dört tane matrisi geometrik yorumlarıyla birlikte ele aldık.
References
- T. A. Ell and S. J. Sangwine, Quaternion involutions and anti-involutions, Computers & Mathematics with Applications, 53 (2007), pp. 137-143.
- W.R. Hamilton, On a new species of imaginary quantities connected with the theory of quaternions, Proceedings of the Royal Irish Academy 2 (1844), pp. 424–434.
- J. B. Kuipers, Quaternions and Rotation Sequences, Published by Princenton University Press, New Jersey, 1999.
- J. P. Ward, Quaternions and Cayley Algebrs and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
- O. P. Agrawal, Hamilton Operatorsand Dualnumber-quaternions in Spatial Kinematic, Mech. Mach. Theory, 22 (1987), pp. 569-575.
- E. Ata and Y. Yayli, Dual Unitary Matrices and Unit Dual Quaternions, Differential Geometry Dynamical Systems, 10 (2008), pp. 1-12.
- M. Bekar and Y. Yayli, Dual Quaternion Involutions and Anti-Involutions, Advances in Applied Clifford Algebras 23 (2013) , pp. 577–592.
- M. Hazewinkel (Ed.), Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ‘Mathematical Encyclopaedia’, Kluwer, Dordrecht, 1988-1994.
Abstract
Rigid-body (screw) motions in three-dimensional
Euclidean space can be represented by involution (resp.
anti-involution) mappings obtained by dual-quaternions which are self-inverse
and homomorphic (resp. anti-homomrphic) linear mappings. In this paper, we will
represent four dual-quaternion matrices with their geometrical meanings; two of
them correspond to involution mappings, while the other two correspond to
anti-involution mappings.
References
- T. A. Ell and S. J. Sangwine, Quaternion involutions and anti-involutions, Computers & Mathematics with Applications, 53 (2007), pp. 137-143.
- W.R. Hamilton, On a new species of imaginary quantities connected with the theory of quaternions, Proceedings of the Royal Irish Academy 2 (1844), pp. 424–434.
- J. B. Kuipers, Quaternions and Rotation Sequences, Published by Princenton University Press, New Jersey, 1999.
- J. P. Ward, Quaternions and Cayley Algebrs and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
- O. P. Agrawal, Hamilton Operatorsand Dualnumber-quaternions in Spatial Kinematic, Mech. Mach. Theory, 22 (1987), pp. 569-575.
- E. Ata and Y. Yayli, Dual Unitary Matrices and Unit Dual Quaternions, Differential Geometry Dynamical Systems, 10 (2008), pp. 1-12.
- M. Bekar and Y. Yayli, Dual Quaternion Involutions and Anti-Involutions, Advances in Applied Clifford Algebras 23 (2013) , pp. 577–592.
- M. Hazewinkel (Ed.), Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ‘Mathematical Encyclopaedia’, Kluwer, Dordrecht, 1988-1994.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | December 2, 2016 |
| Published in Issue | Year 2016 Volume: 11 Issue: 2 |
