Siacci's Theorem According to Darboux Frame

Abstract

The resolution of the acceleration vector of rigid body moving along a space curve is well known thanks to Siacci [1]. In this resolution,the acceleration vector is stated as the sum of two special oblique components in the osculating plane of the point of the curve. In this paper, we have studied the Siacci's theorem for the curves on regular surfaces in 3-dimensional Euclidean space. Also, an example is given for a helix lying on a cylinder.