In this article, quaternions, which is a preferred and elegant method for expressing spherical rotations, are generalized with the help of generalized scalar product spaces, and elliptical rotations on any given ellipsoid are examined by them. To this end, firstly, we define the generalized elliptical scalar product space which accepts the given ellipsoid as a sphere and determines skew symmetric matrices, and the generalized vector product related to this scalar product space. Then we define the generalized elliptical quaternions by using these notions. Finally, elliptical rotations on any ellipsoid in the space are examined by using the unit generalized elliptical quaternions. The formulas and results obtained are supported with numerical examples.
Generalized elliptical scalar product, generalized elliptical vector product, generalized elliptical quaternion, rotation matrix, elliptical rotation
ÇOLAKOĞLU, HARUN BARIŞ and ÖZDEMİR, MUSTAFA
"Generalized elliptical quaternions with some applications,"
Turkish Journal of Mathematics: Vol. 47:
1, Article 23.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss1/23