Some Characterizations on Geodesic, Asymptotic and Slant Helical Trajectories According to PAFORS

Authors : Kahraman Esen ÖZEN, Murat TOSUN

Pages : 74-90

Doi:10.47087/mjm.926078

View : 15 | Download : 10

Publication Date : 2021-10-30

Article Type : Research Paper

Abstract :In this paper, we study the geodesic, asymptotic and slant helical trajectories according to PAFORS in three-dimensional Euclidean space and give some characterizations on them. Also, we explain how we determine the helix axis for slant helical trajectories insert ignore into journalissuearticles values(according to PAFORS);. Moreover, we develop a method which enables us to find the slant helical trajectory insert ignore into journalissuearticles values(if exists); lying on a given implicit surface which accepts a given fixed unit direction as an axis and a given angle as the constant angle. This method also gives information when the desired slant helical trajectory does not exist. The results obtained here involve some differential and partial differential equations or they are based on these equations. The aforementioned results are new contributions to the field and they may be useful in some specific applications of particle kinematics and differential geometry.
Keywords : kinematics of a particle, regular surfaces, slant helix, differential equations, initial value problem