On Elliptical Motions on a General Ellipsoid

ÇOLAKOĞLU H. B., ÖZDEMİR M.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.20, sa.3, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00009-023-02353-x
  • Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Cayley map, elliptical rotation matrix, Generalized scalar product spaces, Householder map, Rodrigues formula
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we determine elliptical motions that occur on any given ellipsoid in 3D space without using affine transformations. To this end, first, we define the generalized Euclidean inner product whose sphere is the given ellipsoid, and determine skew symmetric matrices and the generalized vector product related to the 3D generalized Euclidean inner product space. Finally, we generate elliptical rotation matrices in 3D generalized Euclidean space using the famous Rodrigues, Cayley, and Householder methods. The formulas and results obtained are supported with numerical examples. We also give an algorithm for generalized elliptical rotation.