An Alternative Approach to Elliptical Motion

Creative Commons License

ÖZDEMİR M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, cilt.26, sa.1, ss.279-304, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 26 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s00006-015-0592-3
  • Dergi Adı: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.279-304
  • Anahtar Kelimeler: Elliptic quaternion, Rotation matrices, Rodrigues formula, Cayley transformation, Householder transformation, ROTATION MATRIX, REAL, PRODUCT, FORMULA, TIME
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an ellipsoid using elliptic inner product and elliptic vector product. To generate an elliptical rotation matrix, first we define an elliptical ortogonal matrix and an elliptical skew symmetric matrix using the associated inner product. Then we use elliptic versions of the famous Rodrigues, Cayley, and Householder methods to construct an elliptical rotation matrix. Finally, we define elliptic quaternions and generate an elliptical rotation matrix using those quaternions. Each method is proven and is provided with several numerical examples.