Elliptical rotations with hybrid numbers
İskender, Öztürk
Elliptical rotations with hybrid numbers - Vol.55(1), Mar - New Delhi Springer 2024 - 23-39p.
In this article, some geometric interpretations and applications of hybrid numbers, which unify elliptic, hyperbolic and dual numbers, are given. First, the definition of an elliptical (complex) plane is given, and elliptic rotations in this plane are examined using hybrid number multiplication. Also, mutually orthogonal planar elliptical rotations in four-dimensional space are discussed. At last, matrix forms of a non-parabolic rotation transformation are expressed, and Rodrigues and Cayley rotation transformations for an elliptical hybrid vector are proved.
Humanities and Applied Sciences
Elliptical rotations with hybrid numbers - Vol.55(1), Mar - New Delhi Springer 2024 - 23-39p.
In this article, some geometric interpretations and applications of hybrid numbers, which unify elliptic, hyperbolic and dual numbers, are given. First, the definition of an elliptical (complex) plane is given, and elliptic rotations in this plane are examined using hybrid number multiplication. Also, mutually orthogonal planar elliptical rotations in four-dimensional space are discussed. At last, matrix forms of a non-parabolic rotation transformation are expressed, and Rodrigues and Cayley rotation transformations for an elliptical hybrid vector are proved.
Humanities and Applied Sciences