Mathematical Methods in the Applied Sciences, 2021 (SCI-Expanded)
In this work, we consider the Rotation Minimizing frame attached to a spatial curve to explain the kinematics of the accretive growth. Choosing this frame provides minimal twist along the cell tracks and makes the angular velocity of the local basis minimal. By this method, we obtain more suitable models of some biological beings. Also, we use the quaternions in E3 to model the kinematics of the accretive growth in a practical way. Moreover, we give the relation between the proposed models.