Dual Kuaterniyon İnvolüsyon Matrislerin Kinematiği

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.

Anahtar Kelimeler:

Reel-kuaterniyon, dual-kuaterniyon, (anti)-involüsyon, vida hareketİ

Kinematics of Dual Quaternion Involution Matrices

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.

Keywords:

Real-quaternion, dual-quaternion, (anti)-involution, rigid-body (screw) motion,

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