DYNAMIC SYSTEM

Abstract

The paper deals with the differential geometry problem of finding the Cartesian coordinates of a curve defined by its own normal and torsion curvatures. Analysing the Serret-Frenet frame kinematics, there are derived the differential equations of its orientation angles. Then, by common geometry tools, there are derived the differential equations of the spherical coordinates, which are used to determine the cartesian ones. The result thus obtained is used for some special cases of intrinsic defined curves. The differential system that generates the coordinates of an intrinsic defined curve is used when we intend to describe in an intrinsic manner the general motion of a rigid body (namely an aircraft or space vehicle).