Multiplicative elliptic quaternions and generating geometric elliptic rotation matrices

Ellipse motion involving an angle about a vector is referred to as elliptical rotation. The purpose of this work is to define a new class of elliptic quaternions, elliptic inner product, and elliptic vector product, which we refer to as multiplicative elliptic quaternions. Then, utilizing those multiplicative elliptic quaternions, we produce a multiplicative elliptical rotation matrix and provide several applications. In the end, the theorems established were presented along geometric and physical applications suitable for the quaternionic structure with the help of Maple. There were also given examples of various applications.