On the Resolution of the Acceleration Vector According to Bishop Frame

In the second half of the 19th century, Siacci investigated the motion of a particle in space under the influence of any forces (Atti R Accad Sci. Torino \textbf{14}(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 (Am Math Monthly \textbf{82}(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.