Null-axis rotation theory for superquadrics via the Gielis superformula
PHYSICA SCRIPTA, cilt.101, sa.31, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 101 Sayı: 31
- Basım Tarihi: 2026
- Doi Numarası: 10.1088/1402-4896/ae8d9d
- Dergi Adı: PHYSICA SCRIPTA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
- Ankara Üniversitesi Adresli: Evet
Özet
In this work, using the superquadric-dependent inner product and an associated vector product via the Gielis superformula, we study rotational dynamics on the superquadric lightcone -1r(phi)2 delta 1x2+1r(phi)2 delta 2y2+1r(phi)2 delta 3z2=0. To handle rotation motion around the null-axis, we derive Rodrigues- and Cayley-type rotation formulas adapted to this geometry. We further introduce a new algebraic structure, termed the superquadric hyperbolic split quaternion with null vector part, which provides a unified representation of superquadric geometry and Lorentzian rotational theory. Explicit matrix representations of the corresponding rotations generated by unit elements of this algebra are obtained. The proposed framework is illustrated through superquadric parabolic rotational models, demonstrating the geometric effects of the superquadric deformation.