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## trenDual Kuaterniyon İnvolüsyon Matrislerin KinematiğiKinematics of Dual Quaternion Involution Matrices

#### Murat BEKAR [1] , Yusuf YAYLI [2]

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.

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.

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Primary Language en Mathematics Makaleler Author: Murat BEKAR (Primary Author)Institution: Süleyman Demirel Üniv.Country: Turkey Author: Yusuf YAYLI Institution: ANKARA ÜNİVERSİTESİCountry: Turkey Publication Date : December 2, 2016
 Bibtex @research article { sdufeffd292271, journal = {Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi}, issn = {}, eissn = {1306-7575}, address = {}, publisher = {Süleyman Demirel University}, year = {2016}, volume = {11}, pages = {121 - 132}, doi = {}, title = {Kinematics of Dual Quaternion Involution Matrices}, key = {cite}, author = {Bekar, Murat and Yaylı, Yusuf} } APA Bekar, M , Yaylı, Y . (2016). Kinematics of Dual Quaternion Involution Matrices . Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi , 11 (2) , 121-132 . Retrieved from https://dergipark.org.tr/en/pub/sdufeffd/issue/27465/292271 MLA Bekar, M , Yaylı, Y . "Kinematics of Dual Quaternion Involution Matrices" . Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 11 (2016 ): 121-132 Chicago Bekar, M , Yaylı, Y . "Kinematics of Dual Quaternion Involution Matrices". Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 11 (2016 ): 121-132 RIS TY - JOUR T1 - Kinematics of Dual Quaternion Involution Matrices AU - Murat Bekar , Yusuf Yaylı Y1 - 2016 PY - 2016 N1 - DO - T2 - Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi JF - Journal JO - JOR SP - 121 EP - 132 VL - 11 IS - 2 SN - -1306-7575 M3 - UR - Y2 - 2016 ER - EndNote %0 Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi Kinematics of Dual Quaternion Involution Matrices %A Murat Bekar , Yusuf Yaylı %T Kinematics of Dual Quaternion Involution Matrices %D 2016 %J Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi %P -1306-7575 %V 11 %N 2 %R %U ISNAD Bekar, Murat , Yaylı, Yusuf . "Kinematics of Dual Quaternion Involution Matrices". Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi 11 / 2 (December 2016): 121-132 . AMA Bekar M , Yaylı Y . Kinematics of Dual Quaternion Involution Matrices. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi. 2016; 11(2): 121-132. Vancouver Bekar M , Yaylı Y . Kinematics of Dual Quaternion Involution Matrices. Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi. 2016; 11(2): 121-132. IEEE M. Bekar and Y. Yaylı , "Kinematics of Dual Quaternion Involution Matrices", Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, vol. 11, no. 2, pp. 121-132, Dec. 2016

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