A New Moving Frame for Trajectories on Regular Surfaces

Authors : Kahraman Esen ÖZEN, Murat TOSUN

Pages : 20-34

View : 12 | Download : 8

Publication Date : 2021-06-02

Article Type : Research Paper

Abstract :In this study, we introduce a new moving frame on regular surfaces for trajectories with non-vanishing angular momentum and give the angular velocity vector for this frame. Then, we consider the special trajectories generated by Smarandache curves according to this frame in three-dimensional Euclidean space and investigate the Serret-Frenet apparatus of them. Moreover, we provide an illustrative example explaining how this frame is constructed and how the aforementioned special trajectories are generated. This moving frame is a new contribution to the field and we expect that it will be useful in some specific applications of differential geometry and kinematics in the future.
Keywords : Kinematics of a particle, Moving frame, Regular surfaces, Angular momentum, Smarandache curves