On the Resolution of the Acceleration Vector According to Bishop Frame

Authors : Kahraman Esen ÖZEN, Murat TOSUN

Pages : 26-32

Doi:10.32323/ujma.818071

View : 18 | Download : 11

Publication Date : 2021-03-22

Article Type : Research Paper

Abstract :In the second half of the 19th century, Siacci investigated the motion of a particle in space under the influence of any forces insert ignore into journalissuearticles values(Atti R Accad Sci. Torino \textbf{14}insert ignore into journalissuearticles values(1879););. In this study, Siacci obtained a resolution of the acceleration vector which is very useful when the angular momentum is conserved. On the other hand, Bishop introduced the Bishop frame which is well defined for every curves and so very convenient for mathematical researches in the third quarter of the 20th century insert ignore into journalissuearticles values(Am Math Monthly \textbf{82}insert ignore into journalissuearticles values(1975););. In this study, we discuss the Siacci`s resolution of the acceleration vector according to Bishop frame of the trajectory of the moving particle. Also, we provide an illustrative example for the obtained results.
Keywords : Kinematics of a particle, Plane and space curves, Bishop frame, Siacci