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Abstract
Quaternions, particularly the double and dual forms, are important for the representation rotations and more general rigid-body motions. The Cayley factorization allows a real orthogonal 44 matrix to be expressed as the product of two isoclinic matrices and this is a the key part of the underlying theory and a useful tool in applications. An isoclinic matrix is defined in terms of its representation of a rotation in four-dimensional space. This paper looks at characterizing such a matrix as the sum of a skew symmetric matrix and a scalar multiple of the identity whose product with its own transpose is diagonal. This removes the need to deal with its geometric properties and provides a means for showing the existence of the Cayley factorization.
Original language | English |
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Journal | Institution of Mechanical Engineers. Proceedings. Part G: Journal of Aerospace Engineering |
Early online date | 28 Oct 2015 |
DOIs | |
Publication status | Published - 2015 |
Keywords
- Quaternion
- double quaternion
- dual quaternion
- Cayley factorization
- rigid-body transform
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Dive into the research topics of 'Characterizing isoclinic matrices and the Cayley Factorization'. Together they form a unique fingerprint.Projects
- 1 Finished
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Algebraic modelling of 5 axis tool path motions
Cripps, B.
Engineering & Physical Science Research Council
31/03/14 → 30/03/17
Project: Research Councils