Quaternion-Based Representation of Rotation Minimizing Motions in Euclidean 3-space
Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, cilt.34, sa.1, ss.5-28, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 34 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.2478/auom-2026-0001
- Dergi Adı: Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals
- Sayfa Sayıları: ss.5-28
- Anahtar Kelimeler: angular velocity, curves, quaternionic helix, Quaternions, rotation minimizing motions
- Ankara Üniversitesi Adresli: Evet
Özet
This paper presents a quaternion-based framework for constructing rotation-minimizing motions in Euclidean 3-space, formulated via quaternion operator. By introducing a novel quaternion operator, we derive angular velocity representations directly from the quaternion derivative and its conjugate, enabling smooth and minimal-rotation motion. The proposed approach generates rotation-minimizing motions whose trajectories are aligned with the orbits of a given spatial curve, and it offers a convenient mechanism to compute the corresponding quaternion representation when the orbit and a spatial position are specified. The effectiveness of the method is demonstrated through numerical experiments involving the spherical indicatricestangent, normal, and binormal-of space curves. Additionally, we provide a geometric characterization of quaternionic helical curves with respect to the tangential image T, highlighting the theoretical and practical implications of the proposed model in motion design and spatial kinematics.